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reference:

step	inference rule	input	feed	output	validity (as per SymPy)
20	ID: 111886; change variable X to Y number of inputs: 1; feeds: 2; outputs: 1 Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.	9988949211 $(\sin(x))^2=\frac{1 - \cos(2 x)}{2}$	0004934845 $x$ 0009484724 $\frac{n \pi}{W}x$	7575738420 $\left(\sin\left(\frac{n \pi}{W}x\right) \right)^2=\frac{1-\cos\left(2\frac{n \pi}{W}x\right)}{2}$	LHS diff is 0 RHS diff is cos(2pdg0001464pdg0001592pdg0003141/pdg0002523)/2 - cos(2pdg0001592pdg0003141pdg0004037/pdg0002523)/2
32	ID: 111524; square root both sides number of inputs: 1; feeds: 0; outputs: 2 Take the square root of both sides of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2} and Eq.~\\ref{eq:#3}.	8485867742 $\frac{2}{W}=a^2$		9485747245 $\sqrt{\frac{2}{W}}=a$ 9485747246 $-\sqrt{\frac{2}{W}}=a$	recognized infrule but not yet supported
2	ID: 111237; declare guess solution number of inputs: 1; feeds: 0; outputs: 1 Judicious choice as a guessed solution to Eq.~\\ref{eq:#1} is Eq.~\\ref{eq:#2},	5727578862 $\frac{d^2}{dx^2} \psi(x)=-k^2 \psi(x)$		8582885111 $\psi(x)=a \sin(kx) + b \cos(kx)$	no validation is available for declarations
33	ID: 111556; substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	9485747245 $\sqrt{\frac{2}{W}}=a$ 2944838499 $\psi(x)=a \sin(\frac{n \pi}{W} x)$		9393939991 $\psi(x)=-\sqrt{\frac{2}{W}} \sin\left(\frac{n \pi}{W} x\right)$	LHS diff is 0 RHS diff is pdg0009139sin(pdg0001592pdg0003141pdg0004037/pdg0002523) + sqrt(2)sqrt(1/pdg0002523)sin(pdg0001464pdg0001592*pdg0003141/pdg0002523)
27	ID: 111886; change variable X to Y number of inputs: 1; feeds: 2; outputs: 1 Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.	5857434758 $\int a dx=a x$	0002929944 $1/2$ 0004948585 $a$	8575746378 $\int \frac{1}{2} dx=\frac{1}{2} x$	Type Tuple cannot be instantiated; use tuple() instead
38	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	8575748999 $\frac{d^2}{dx^2} \left(a \sin(k x) + b \cos(k x) \right)=-k^2 \left(a \sin(kx) + b \cos(kx) \right)$		8485757728 $a \frac{d^2}{dx^2}\sin(kx) + b \frac{d^2}{dx^2}\cos(k x)=-a k^2 \sin(kx) + -b k^2 \cos(kx)$	invalid syntax (<string>, line 0)
26	ID: 111299; declare identity number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an identity.			5857434758 $\int a dx=a x$	no validation is available for declarations
24	ID: 111299; declare identity number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an identity.			0948572140 $\int \cos(a x) dx=\frac{1}{a}\sin(a x)$	no validation is available for declarations
28	ID: 111556; substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	8575746378 $\int \frac{1}{2} dx=\frac{1}{2} x$ 1202310110 $\frac{1}{a^2}=\int_0^W \frac{1}{2} dx - \frac{1}{2} \int_0^W \cos\left(2\frac{n \pi}{W}x\right) dx$		1202312210 $\frac{1}{a^2}=\frac{1}{2}W - \frac{1}{2} \int_0^W \cos\left(2\frac{n \pi}{W}x\right) dx$	Type Tuple cannot be instantiated; use tuple() instead
34	ID: 111556; substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	2944838499 $\psi(x)=a \sin(\frac{n \pi}{W} x)$ 9485747246 $-\sqrt{\frac{2}{W}}=a$		9393939992 $\psi(x)=\sqrt{\frac{2}{W}} \sin\left(\frac{n \pi}{W} x\right)$	LHS diff is -sqrt(2)sqrt(1/pdg0002523) - pdg0009489(pdg0001464) RHS diff is pdg0009139 - sqrt(2)sqrt(1/pdg0002523)sin(pdg0001464pdg0001592*pdg0003141/pdg0002523)
23	ID: 111581; expand integrand number of inputs: 1; feeds: 0; outputs: 1 Expand integrand of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	9858028950 $\frac{1}{a^2}=\int_0^W \frac{1-\cos\left(2\frac{n \pi}{W}x\right)}{2} dx$		1202310110 $\frac{1}{a^2}=\int_0^W \frac{1}{2} dx - \frac{1}{2} \int_0^W \cos\left(2\frac{n \pi}{W}x\right) dx$	recognized infrule but not yet supported
13	ID: 111493; normalization condition number of inputs: 0; feeds: 0; outputs: 1 Normalization condition is Eq.~\\ref{eq:#1}.			1934748140 $\int \|\psi(x)\|^2 dx=1$	no validation is available for assumptions
17	ID: 111556; substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	4857472413 $1=\int \psi(x)\psi(x)^* dx$ 2944838499 $\psi(x)=a \sin(\frac{n \pi}{W} x)$		0203024440 $1=\int_0^W a \sin\left(\frac{n \pi}{W} x\right) \psi(x)^* dx$	invalid syntax (<string>, line 0)
25	ID: 111886; change variable X to Y number of inputs: 1; feeds: 2; outputs: 1 Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.	0948572140 $\int \cos(a x) dx=\frac{1}{a}\sin(a x)$	0009485858 $\frac{2n\pi}{W}$ 0004831494 $a$	7564894985 $\int \cos\left(\frac{2n\pi}{W} x\right) dx=\frac{W}{2n\pi}\sin\left(\frac{2n\pi}{W} x\right)$	Type Tuple cannot be instantiated; use tuple() instead
15	ID: 111268; swap LHS with RHS number of inputs: 1; feeds: 0; outputs: 1 Swap LHS of Eq.~\\ref{eq:#1} with RHS; yields Eq.~\\ref{eq:#2}.	1934748140 $\int \|\psi(x)\|^2 dx=1$		8572657110 $1=\int \|\psi(x)\|^2 dx$	Type Tuple cannot be instantiated; use tuple() instead
37	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	8582885111 $\psi(x)=a \sin(kx) + b \cos(kx)$ 5727578862 $\frac{d^2}{dx^2} \psi(x)=-k^2 \psi(x)$		8575748999 $\frac{d^2}{dx^2} \left(a \sin(k x) + b \cos(k x) \right)=-k^2 \left(a \sin(kx) + b \cos(kx) \right)$	invalid syntax (<string>, line 0)
18	ID: 111556; substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	0203024440 $1=\int_0^W a \sin\left(\frac{n \pi}{W} x\right) \psi(x)^* dx$ 8849289982 $\psi(x)^*=a \sin(\frac{n \pi}{W} x)$		8889444440 $1=\int_0^W a^2 \left(\sin\left(\frac{n \pi}{W} x\right) \right)^2 dx$	Type Tuple cannot be instantiated; use tuple() instead
14	ID: 111996; conjugate function X number of inputs: 1; feeds: 1; outputs: 1 Conjugate $#1$ in Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	2944838499 $\psi(x)=a \sin(\frac{n \pi}{W} x)$	0009587738 $\psi$	8849289982 $\psi(x)^*=a \sin(\frac{n \pi}{W} x)$	recognized infrule but not yet supported
31	ID: 111182; multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	4857475848 $\frac{1}{a^2}=\frac{W}{2}$	0009485857 $a^2\frac{2}{W}$	8485867742 $\frac{2}{W}=a^2$	valid
22	ID: 111975; divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	8576785890 $1=\int_0^W a^2 \frac{1-\cos\left(2\frac{n \pi}{W}x\right)}{2} dx$	0000040490 $a^2$	9858028950 $\frac{1}{a^2}=\int_0^W \frac{1-\cos\left(2\frac{n \pi}{W}x\right)}{2} dx$	Type Tuple cannot be instantiated; use tuple() instead
40	ID: 111345; claim LHS equals RHS number of inputs: 1; feeds: 0; outputs: 0 Thus we see that LHS of Eq.~\\ref{eq:#1} is equal to RHS.	8484544728 $-a k^2\sin(k x) + -b k^2\cos(k x)=-a k^2 \sin(kx) + -b k^2 \cos(k x)$			invalid syntax (<string>, line 0)
16	ID: 111166; expand magnitude to conjugate number of inputs: 1; feeds: 1; outputs: 1 Expand $#1$ in Eq.~\\ref{eq:#2} with conjugate; yields Eq.~\\ref{eq:#3}.	8572657110 $1=\int \|\psi(x)\|^2 dx$	0009458842 $\psi(x)$	4857472413 $1=\int \psi(x)\psi(x)^* dx$	recognized infrule but not yet supported
35	ID: 111341; declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\\ref{eq:#1} is one of the final equations.	9393939992 $\psi(x)=\sqrt{\frac{2}{W}} \sin\left(\frac{n \pi}{W} x\right)$			no validation is available for declarations
30	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	0439492440 $\frac{1}{a^2}=\frac{1}{2}W - \frac{1}{2}\left. \frac{W}{2n\pi}\sin\left(\frac{2n\pi}{W} x\right) \right\|_0^W$		4857475848 $\frac{1}{a^2}=\frac{W}{2}$	LHS diff is 0 RHS diff is -pdg0002523sin(2pdg0001592pdg0003141pdg0004037/pdg0002523)/(4pdg0001592pdg0003141)
19	ID: 111299; declare identity number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an identity.			9988949211 $(\sin(x))^2=\frac{1 - \cos(2 x)}{2}$	no validation is available for declarations
29	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	1202312210 $\frac{1}{a^2}=\frac{1}{2}W - \frac{1}{2} \int_0^W \cos\left(2\frac{n \pi}{W}x\right) dx$ 7564894985 $\int \cos\left(\frac{2n\pi}{W} x\right) dx=\frac{W}{2n\pi}\sin\left(\frac{2n\pi}{W} x\right)$		0439492440 $\frac{1}{a^2}=\frac{1}{2}W - \frac{1}{2}\left. \frac{W}{2n\pi}\sin\left(\frac{2n\pi}{W} x\right) \right\|_0^W$	Type Tuple cannot be instantiated; use tuple() instead
5	ID: 111355; LHS of expr 1 equals LHS of expr 2 number of inputs: 2; feeds: 0; outputs: 1 LHS of Eq.~\\ref{eq:#1} is equal to LHS of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	9585727710 $\psi(x=0)=0$ 8582885111 $\psi(x)=a \sin(kx) + b \cos(kx)$		8577275751 $0=a \sin(0) + b\cos(0)$	input diff is -pdg0009489(pdg0004037) + pdg0009489(Eq(pdg0001464, 0)) diff is 0 diff is pdg0001939cos(pdg0004037pdg0005321) - pdg0001939 + pdg0009139sin(pdg0004037pdg0005321)
7	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	1293913110 $0=b$ 8582885111 $\psi(x)=a \sin(kx) + b \cos(kx)$		9059289981 $\psi(x)=a \sin(k x)$	invalid syntax (<string>, line 0)
3	ID: 111802; boundary condition for expression number of inputs: 1; feeds: 0; outputs: 1 A boundary condition for Eq.~\\ref{eq:#1} is Eq.~\\ref{eq:#2}	5727578862 $\frac{d^2}{dx^2} \psi(x)=-k^2 \psi(x)$		9585727710 $\psi(x=0)=0$	no validation is available for assumptions
4	ID: 111802; boundary condition for expression number of inputs: 1; feeds: 0; outputs: 1 A boundary condition for Eq.~\\ref{eq:#1} is Eq.~\\ref{eq:#2}	5727578862 $\frac{d^2}{dx^2} \psi(x)=-k^2 \psi(x)$		9495857278 $\psi(x=W)=0$	no validation is available for assumptions
10	ID: 111698; expr 1 is true under condition expr 2 number of inputs: 2; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is valid when Eq.~\\ref{eq:#2} occurs; yields Eq.~\\ref{eq:#3}.	1857710291 $0=a \sin(n \pi)$ 1020010291 $0=a \sin(k W)$		1010923823 $k W=n \pi$	recognized infrule but not yet supported
9	ID: 111299; declare identity number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an identity.			1857710291 $0=a \sin(n \pi)$	no validation is available for declarations
12	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	9059289981 $\psi(x)=a \sin(k x)$ 1858772113 $k=\frac{n \pi}{W}$		2944838499 $\psi(x)=a \sin(\frac{n \pi}{W} x)$	invalid syntax (<string>, line 0)
6	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	8577275751 $0=a \sin(0) + b\cos(0)$		1293913110 $0=b$	valid
1	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			5727578862 $\frac{d^2}{dx^2} \psi(x)=-k^2 \psi(x)$	no validation is available for declarations
21	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	8889444440 $1=\int_0^W a^2 \left(\sin\left(\frac{n \pi}{W} x\right) \right)^2 dx$ 7575738420 $\left(\sin\left(\frac{n \pi}{W}x\right) \right)^2=\frac{1-\cos\left(2\frac{n \pi}{W}x\right)}{2}$		8576785890 $1=\int_0^W a^2 \frac{1-\cos\left(2\frac{n \pi}{W}x\right)}{2} dx$	Type Tuple cannot be instantiated; use tuple() instead
11	ID: 111975; divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	1010923823 $k W=n \pi$	0001334112 $W$	1858772113 $k=\frac{n \pi}{W}$	valid
39	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	8485757728 $a \frac{d^2}{dx^2}\sin(kx) + b \frac{d^2}{dx^2}\cos(k x)=-a k^2 \sin(kx) + -b k^2 \cos(kx)$		8484544728 $-a k^2\sin(k x) + -b k^2\cos(k x)=-a k^2 \sin(kx) + -b k^2 \cos(k x)$	invalid syntax (<string>, line 0)
8	ID: 111355; LHS of expr 1 equals LHS of expr 2 number of inputs: 2; feeds: 0; outputs: 1 LHS of Eq.~\\ref{eq:#1} is equal to LHS of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	9495857278 $\psi(x=W)=0$ 9059289981 $\psi(x)=a \sin(k x)$		1020010291 $0=a \sin(k W)$	invalid syntax (<string>, line 0)

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timing of Neo4j queries:

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step	inference rule	input	feed	output	validity (as per SymPy)
20	ID: 111886; change variable X to Y number of inputs: 1; feeds: 2; outputs: 1 Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.	9988949211 \((\sin(x))^2=\frac{1 - \cos(2 x)}{2}\)	0004934845 \(x\) 0009484724 \(\frac{n \pi}{W}x\)	7575738420 \(\left(\sin\left(\frac{n \pi}{W}x\right) \right)^2=\frac{1-\cos\left(2\frac{n \pi}{W}x\right)}{2}\)	LHS diff is 0 RHS diff is cos(2pdg0001464pdg0001592pdg0003141/pdg0002523)/2 - cos(2pdg0001592pdg0003141pdg0004037/pdg0002523)/2
32	ID: 111524; square root both sides number of inputs: 1; feeds: 0; outputs: 2 Take the square root of both sides of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2} and Eq.~\\ref{eq:#3}.	8485867742 \(\frac{2}{W}=a^2\)		9485747245 \(\sqrt{\frac{2}{W}}=a\) 9485747246 \(-\sqrt{\frac{2}{W}}=a\)	recognized infrule but not yet supported
2	ID: 111237; declare guess solution number of inputs: 1; feeds: 0; outputs: 1 Judicious choice as a guessed solution to Eq.~\\ref{eq:#1} is Eq.~\\ref{eq:#2},	5727578862 \(\frac{d^2}{dx^2} \psi(x)=-k^2 \psi(x)\)		8582885111 \(\psi(x)=a \sin(kx) + b \cos(kx)\)	no validation is available for declarations
33	ID: 111556; substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	9485747245 \(\sqrt{\frac{2}{W}}=a\) 2944838499 \(\psi(x)=a \sin(\frac{n \pi}{W} x)\)		9393939991 \(\psi(x)=-\sqrt{\frac{2}{W}} \sin\left(\frac{n \pi}{W} x\right)\)	LHS diff is 0 RHS diff is pdg0009139sin(pdg0001592pdg0003141pdg0004037/pdg0002523) + sqrt(2)sqrt(1/pdg0002523)sin(pdg0001464pdg0001592*pdg0003141/pdg0002523)
27	ID: 111886; change variable X to Y number of inputs: 1; feeds: 2; outputs: 1 Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.	5857434758 \(\int a dx=a x\)	0002929944 \(1/2\) 0004948585 \(a\)	8575746378 \(\int \frac{1}{2} dx=\frac{1}{2} x\)	Type Tuple cannot be instantiated; use tuple() instead
38	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	8575748999 \(\frac{d^2}{dx^2} \left(a \sin(k x) + b \cos(k x) \right)=-k^2 \left(a \sin(kx) + b \cos(kx) \right)\)		8485757728 \(a \frac{d^2}{dx^2}\sin(kx) + b \frac{d^2}{dx^2}\cos(k x)=-a k^2 \sin(kx) + -b k^2 \cos(kx)\)	invalid syntax (<string>, line 0)
26	ID: 111299; declare identity number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an identity.			5857434758 \(\int a dx=a x\)	no validation is available for declarations
24	ID: 111299; declare identity number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an identity.			0948572140 \(\int \cos(a x) dx=\frac{1}{a}\sin(a x)\)	no validation is available for declarations
28	ID: 111556; substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	8575746378 \(\int \frac{1}{2} dx=\frac{1}{2} x\) 1202310110 \(\frac{1}{a^2}=\int_0^W \frac{1}{2} dx - \frac{1}{2} \int_0^W \cos\left(2\frac{n \pi}{W}x\right) dx\)		1202312210 \(\frac{1}{a^2}=\frac{1}{2}W - \frac{1}{2} \int_0^W \cos\left(2\frac{n \pi}{W}x\right) dx\)	Type Tuple cannot be instantiated; use tuple() instead
34	ID: 111556; substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	2944838499 \(\psi(x)=a \sin(\frac{n \pi}{W} x)\) 9485747246 \(-\sqrt{\frac{2}{W}}=a\)		9393939992 \(\psi(x)=\sqrt{\frac{2}{W}} \sin\left(\frac{n \pi}{W} x\right)\)	LHS diff is -sqrt(2)sqrt(1/pdg0002523) - pdg0009489(pdg0001464) RHS diff is pdg0009139 - sqrt(2)sqrt(1/pdg0002523)sin(pdg0001464pdg0001592*pdg0003141/pdg0002523)
23	ID: 111581; expand integrand number of inputs: 1; feeds: 0; outputs: 1 Expand integrand of Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	9858028950 \(\frac{1}{a^2}=\int_0^W \frac{1-\cos\left(2\frac{n \pi}{W}x\right)}{2} dx\)		1202310110 \(\frac{1}{a^2}=\int_0^W \frac{1}{2} dx - \frac{1}{2} \int_0^W \cos\left(2\frac{n \pi}{W}x\right) dx\)	recognized infrule but not yet supported
13	ID: 111493; normalization condition number of inputs: 0; feeds: 0; outputs: 1 Normalization condition is Eq.~\\ref{eq:#1}.			1934748140 \(\int \|\psi(x)\|^2 dx=1\)	no validation is available for assumptions
17	ID: 111556; substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	4857472413 \(1=\int \psi(x)\psi(x)^* dx\) 2944838499 \(\psi(x)=a \sin(\frac{n \pi}{W} x)\)		0203024440 \(1=\int_0^W a \sin\left(\frac{n \pi}{W} x\right) \psi(x)^* dx\)	invalid syntax (<string>, line 0)
25	ID: 111886; change variable X to Y number of inputs: 1; feeds: 2; outputs: 1 Change variable $#1$ to $#2$ in Eq.~\\ref{eq:#3}; yields Eq.~\\ref{eq:#4}.	0948572140 \(\int \cos(a x) dx=\frac{1}{a}\sin(a x)\)	0009485858 \(\frac{2n\pi}{W}\) 0004831494 \(a\)	7564894985 \(\int \cos\left(\frac{2n\pi}{W} x\right) dx=\frac{W}{2n\pi}\sin\left(\frac{2n\pi}{W} x\right)\)	Type Tuple cannot be instantiated; use tuple() instead
15	ID: 111268; swap LHS with RHS number of inputs: 1; feeds: 0; outputs: 1 Swap LHS of Eq.~\\ref{eq:#1} with RHS; yields Eq.~\\ref{eq:#2}.	1934748140 \(\int \|\psi(x)\|^2 dx=1\)		8572657110 \(1=\int \|\psi(x)\|^2 dx\)	Type Tuple cannot be instantiated; use tuple() instead
37	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	8582885111 \(\psi(x)=a \sin(kx) + b \cos(kx)\) 5727578862 \(\frac{d^2}{dx^2} \psi(x)=-k^2 \psi(x)\)		8575748999 \(\frac{d^2}{dx^2} \left(a \sin(k x) + b \cos(k x) \right)=-k^2 \left(a \sin(kx) + b \cos(kx) \right)\)	invalid syntax (<string>, line 0)
18	ID: 111556; substitute LHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute LHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	0203024440 \(1=\int_0^W a \sin\left(\frac{n \pi}{W} x\right) \psi(x)^* dx\) 8849289982 \(\psi(x)^*=a \sin(\frac{n \pi}{W} x)\)		8889444440 \(1=\int_0^W a^2 \left(\sin\left(\frac{n \pi}{W} x\right) \right)^2 dx\)	Type Tuple cannot be instantiated; use tuple() instead
14	ID: 111996; conjugate function X number of inputs: 1; feeds: 1; outputs: 1 Conjugate $#1$ in Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	2944838499 \(\psi(x)=a \sin(\frac{n \pi}{W} x)\)	0009587738 \(\psi\)	8849289982 \(\psi(x)^*=a \sin(\frac{n \pi}{W} x)\)	recognized infrule but not yet supported
31	ID: 111182; multiply both sides by number of inputs: 1; feeds: 1; outputs: 1 Multiply both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	4857475848 \(\frac{1}{a^2}=\frac{W}{2}\)	0009485857 \(a^2\frac{2}{W}\)	8485867742 \(\frac{2}{W}=a^2\)	valid
22	ID: 111975; divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	8576785890 \(1=\int_0^W a^2 \frac{1-\cos\left(2\frac{n \pi}{W}x\right)}{2} dx\)	0000040490 \(a^2\)	9858028950 \(\frac{1}{a^2}=\int_0^W \frac{1-\cos\left(2\frac{n \pi}{W}x\right)}{2} dx\)	Type Tuple cannot be instantiated; use tuple() instead
40	ID: 111345; claim LHS equals RHS number of inputs: 1; feeds: 0; outputs: 0 Thus we see that LHS of Eq.~\\ref{eq:#1} is equal to RHS.	8484544728 \(-a k^2\sin(k x) + -b k^2\cos(k x)=-a k^2 \sin(kx) + -b k^2 \cos(k x)\)			invalid syntax (<string>, line 0)
16	ID: 111166; expand magnitude to conjugate number of inputs: 1; feeds: 1; outputs: 1 Expand $#1$ in Eq.~\\ref{eq:#2} with conjugate; yields Eq.~\\ref{eq:#3}.	8572657110 \(1=\int \|\psi(x)\|^2 dx\)	0009458842 \(\psi(x)\)	4857472413 \(1=\int \psi(x)\psi(x)^* dx\)	recognized infrule but not yet supported
35	ID: 111341; declare final expression number of inputs: 1; feeds: 0; outputs: 0 Eq.~\\ref{eq:#1} is one of the final equations.	9393939992 \(\psi(x)=\sqrt{\frac{2}{W}} \sin\left(\frac{n \pi}{W} x\right)\)			no validation is available for declarations
30	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	0439492440 \(\frac{1}{a^2}=\frac{1}{2}W - \frac{1}{2}\left. \frac{W}{2n\pi}\sin\left(\frac{2n\pi}{W} x\right) \right\|_0^W\)		4857475848 \(\frac{1}{a^2}=\frac{W}{2}\)	LHS diff is 0 RHS diff is -pdg0002523sin(2pdg0001592pdg0003141pdg0004037/pdg0002523)/(4pdg0001592pdg0003141)
19	ID: 111299; declare identity number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an identity.			9988949211 \((\sin(x))^2=\frac{1 - \cos(2 x)}{2}\)	no validation is available for declarations
29	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	1202312210 \(\frac{1}{a^2}=\frac{1}{2}W - \frac{1}{2} \int_0^W \cos\left(2\frac{n \pi}{W}x\right) dx\) 7564894985 \(\int \cos\left(\frac{2n\pi}{W} x\right) dx=\frac{W}{2n\pi}\sin\left(\frac{2n\pi}{W} x\right)\)		0439492440 \(\frac{1}{a^2}=\frac{1}{2}W - \frac{1}{2}\left. \frac{W}{2n\pi}\sin\left(\frac{2n\pi}{W} x\right) \right\|_0^W\)	Type Tuple cannot be instantiated; use tuple() instead
5	ID: 111355; LHS of expr 1 equals LHS of expr 2 number of inputs: 2; feeds: 0; outputs: 1 LHS of Eq.~\\ref{eq:#1} is equal to LHS of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	9585727710 \(\psi(x=0)=0\) 8582885111 \(\psi(x)=a \sin(kx) + b \cos(kx)\)		8577275751 \(0=a \sin(0) + b\cos(0)\)	input diff is -pdg0009489(pdg0004037) + pdg0009489(Eq(pdg0001464, 0)) diff is 0 diff is pdg0001939cos(pdg0004037pdg0005321) - pdg0001939 + pdg0009139sin(pdg0004037pdg0005321)
7	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	1293913110 \(0=b\) 8582885111 \(\psi(x)=a \sin(kx) + b \cos(kx)\)		9059289981 \(\psi(x)=a \sin(k x)\)	invalid syntax (<string>, line 0)
3	ID: 111802; boundary condition for expression number of inputs: 1; feeds: 0; outputs: 1 A boundary condition for Eq.~\\ref{eq:#1} is Eq.~\\ref{eq:#2}	5727578862 \(\frac{d^2}{dx^2} \psi(x)=-k^2 \psi(x)\)		9585727710 \(\psi(x=0)=0\)	no validation is available for assumptions
4	ID: 111802; boundary condition for expression number of inputs: 1; feeds: 0; outputs: 1 A boundary condition for Eq.~\\ref{eq:#1} is Eq.~\\ref{eq:#2}	5727578862 \(\frac{d^2}{dx^2} \psi(x)=-k^2 \psi(x)\)		9495857278 \(\psi(x=W)=0\)	no validation is available for assumptions
10	ID: 111698; expr 1 is true under condition expr 2 number of inputs: 2; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is valid when Eq.~\\ref{eq:#2} occurs; yields Eq.~\\ref{eq:#3}.	1857710291 \(0=a \sin(n \pi)\) 1020010291 \(0=a \sin(k W)\)		1010923823 \(k W=n \pi\)	recognized infrule but not yet supported
9	ID: 111299; declare identity number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an identity.			1857710291 \(0=a \sin(n \pi)\)	no validation is available for declarations
12	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	9059289981 \(\psi(x)=a \sin(k x)\) 1858772113 \(k=\frac{n \pi}{W}\)		2944838499 \(\psi(x)=a \sin(\frac{n \pi}{W} x)\)	invalid syntax (<string>, line 0)
6	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	8577275751 \(0=a \sin(0) + b\cos(0)\)		1293913110 \(0=b\)	valid
1	ID: 111981; declare initial expression number of inputs: 0; feeds: 0; outputs: 1 Eq.~\\ref{eq:#1} is an initial equation.			5727578862 \(\frac{d^2}{dx^2} \psi(x)=-k^2 \psi(x)\)	no validation is available for declarations
21	ID: 111634; substitute RHS of expr 1 into expr 2 number of inputs: 2; feeds: 0; outputs: 1 Substitute RHS of Eq.~\\ref{eq:#1} into Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	8889444440 \(1=\int_0^W a^2 \left(\sin\left(\frac{n \pi}{W} x\right) \right)^2 dx\) 7575738420 \(\left(\sin\left(\frac{n \pi}{W}x\right) \right)^2=\frac{1-\cos\left(2\frac{n \pi}{W}x\right)}{2}\)		8576785890 \(1=\int_0^W a^2 \frac{1-\cos\left(2\frac{n \pi}{W}x\right)}{2} dx\)	Type Tuple cannot be instantiated; use tuple() instead
11	ID: 111975; divide both sides by number of inputs: 1; feeds: 1; outputs: 1 Divide both sides of Eq.~\\ref{eq:#2} by $#1$; yields Eq.~\\ref{eq:#3}.	1010923823 \(k W=n \pi\)	0001334112 \(W\)	1858772113 \(k=\frac{n \pi}{W}\)	valid
39	ID: 111457; simplify number of inputs: 1; feeds: 0; outputs: 1 Simplify Eq.~\\ref{eq:#1}; yields Eq.~\\ref{eq:#2}.	8485757728 \(a \frac{d^2}{dx^2}\sin(kx) + b \frac{d^2}{dx^2}\cos(k x)=-a k^2 \sin(kx) + -b k^2 \cos(kx)\)		8484544728 \(-a k^2\sin(k x) + -b k^2\cos(k x)=-a k^2 \sin(kx) + -b k^2 \cos(k x)\)	invalid syntax (<string>, line 0)
8	ID: 111355; LHS of expr 1 equals LHS of expr 2 number of inputs: 2; feeds: 0; outputs: 1 LHS of Eq.~\\ref{eq:#1} is equal to LHS of Eq.~\\ref{eq:#2}; yields Eq.~\\ref{eq:#3}.	9495857278 \(\psi(x=W)=0\) 9059289981 \(\psi(x)=a \sin(k x)\)		1020010291 \(0=a \sin(k W)\)	invalid syntax (<string>, line 0)