TSTP Solution File: BOO034-1 by Toma---0.4
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% File : Toma---0.4
% Problem : BOO034-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 18:11:03 EDT 2023
% Result : Unsatisfiable 1.24s 1.53s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : BOO034-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.12/0.35 % Computer : n005.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sun Aug 27 08:05:38 EDT 2023
% 0.20/0.35 % CPUTime :
% 1.24/1.53 % SZS status Unsatisfiable
% 1.24/1.53 % SZS output start Proof
% 1.24/1.53 original problem:
% 1.24/1.53 axioms:
% 1.24/1.53 multiply(multiply(V, W, X), Y, multiply(V, W, Z)) = multiply(V, W, multiply(X, Y, Z))
% 1.24/1.53 multiply(Y, X, X) = X
% 1.24/1.53 multiply(X, X, Y) = X
% 1.24/1.53 multiply(inverse(Y), Y, X) = X
% 1.24/1.53 multiply(X, Y, inverse(Y)) = X
% 1.24/1.53 goal:
% 1.24/1.53 multiply(multiply(a(), inverse(a()), b()), inverse(multiply(multiply(c(), d(), e()), f(), multiply(c(), d(), g()))), multiply(d(), multiply(g(), f(), e()), c())) != b()
% 1.24/1.53 To show the unsatisfiability of the original goal,
% 1.24/1.53 it suffices to show that multiply(multiply(a(), inverse(a()), b()), inverse(multiply(multiply(c(), d(), e()), f(), multiply(c(), d(), g()))), multiply(d(), multiply(g(), f(), e()), c())) = b() (skolemized goal) is valid under the axioms.
% 1.24/1.53 Here is an equational proof:
% 1.24/1.53 0: multiply(multiply(X0, X1, X2), X3, multiply(X0, X1, X4)) = multiply(X0, X1, multiply(X2, X3, X4)).
% 1.24/1.53 Proof: Axiom.
% 1.24/1.53
% 1.24/1.53 1: multiply(X3, X2, X2) = X2.
% 1.24/1.53 Proof: Axiom.
% 1.24/1.53
% 1.24/1.53 2: multiply(X2, X2, X3) = X2.
% 1.24/1.53 Proof: Axiom.
% 1.24/1.53
% 1.24/1.53 4: multiply(X2, X3, inverse(X3)) = X2.
% 1.24/1.53 Proof: Axiom.
% 1.24/1.53
% 1.24/1.53 6: multiply(X5, X6, multiply(X6, X3, X4)) = multiply(X6, X3, multiply(X5, X6, X4)).
% 1.24/1.53 Proof: A critical pair between equations 0 and 1.
% 1.24/1.53
% 1.24/1.53 12: multiply(X5, X6, multiply(inverse(X6), X3, X4)) = multiply(X5, X3, multiply(X5, X6, X4)).
% 1.24/1.53 Proof: A critical pair between equations 0 and 4.
% 1.24/1.53
% 1.24/1.53 16: multiply(X7, X6, multiply(inverse(X6), X7, X4)) = X7.
% 1.24/1.53 Proof: A critical pair between equations 12 and 2.
% 1.24/1.53
% 1.24/1.53 20: multiply(X7, X8, multiply(X5, X7, X8)) = multiply(X5, X7, X8).
% 1.24/1.53 Proof: A critical pair between equations 6 and 1.
% 1.24/1.53
% 1.24/1.53 22: multiply(X7, X8, multiply(inverse(X8), X3, X8)) = multiply(X7, X3, X8).
% 1.24/1.53 Proof: A critical pair between equations 12 and 1.
% 1.24/1.53
% 1.24/1.53 24: multiply(X7, X8, multiply(X8, X3, inverse(X8))) = multiply(X8, X3, X7).
% 1.24/1.53 Proof: A critical pair between equations 6 and 4.
% 1.24/1.53
% 1.24/1.53 30: multiply(inverse(X11), X9, X11) = X9.
% 1.24/1.53 Proof: A critical pair between equations 20 and 16.
% 1.24/1.53
% 1.24/1.53 34: multiply(X9, inverse(X9), X7) = multiply(X7, X9, inverse(X9)).
% 1.24/1.53 Proof: A critical pair between equations 24 and 1.
% 1.24/1.53
% 1.24/1.53 43: multiply(X9, inverse(X9), X7) = X7.
% 1.24/1.53 Proof: Rewrite equation 34,
% 1.24/1.53 lhs with equations []
% 1.24/1.53 rhs with equations [4].
% 1.24/1.53
% 1.24/1.53 44: multiply(X7, X8, X3) = multiply(X7, X3, X8).
% 1.24/1.53 Proof: Rewrite equation 22,
% 1.24/1.53 lhs with equations [30]
% 1.24/1.53 rhs with equations [].
% 1.24/1.53
% 1.24/1.53 46: multiply(X10, X11, inverse(X10)) = X11.
% 1.24/1.53 Proof: A critical pair between equations 44 and 43.
% 1.24/1.53
% 1.24/1.53 58: multiply(X7, X8, X3) = multiply(X8, X3, X7).
% 1.24/1.53 Proof: Rewrite equation 24,
% 1.24/1.53 lhs with equations [46]
% 1.24/1.53 rhs with equations [].
% 1.24/1.53
% 1.24/1.53 59: multiply(multiply(a(), inverse(a()), b()), inverse(multiply(multiply(c(), d(), e()), f(), multiply(c(), d(), g()))), multiply(d(), multiply(g(), f(), e()), c())) = b().
% 1.24/1.53 Proof: Rewrite lhs with equations [43,0,44,58,44,58,44,44,4]
% 1.24/1.53 rhs with equations [].
% 1.24/1.53
% 1.24/1.53 % SZS output end Proof
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