TSTP Solution File: ALG235-1 by Toma---0.4
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% File : Toma---0.4
% Problem : ALG235-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n021.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 16:41:25 EDT 2023
% Result : Unsatisfiable 8.61s 8.90s
% Output : CNFRefutation 8.61s
% 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 : ALG235-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 04:30:13 EDT 2023
% 0.13/0.35 % CPUTime :
% 8.61/8.90 % SZS status Unsatisfiable
% 8.61/8.90 % SZS output start Proof
% 8.61/8.90 original problem:
% 8.61/8.90 axioms:
% 8.61/8.90 mult(A, mult(B, mult(A, B))) = mult(A, B)
% 8.61/8.90 mult(A, mult(B, mult(C, D))) = mult(C, mult(B, mult(A, D)))
% 8.61/8.90 mult(mult(A, mult(B, mult(C, B))), D) = mult(A, mult(D, mult(mult(C, B), D)))
% 8.61/8.90 goal:
% 8.61/8.90 mult(a(), mult(b(), mult(a(), mult(c(), mult(d(), c()))))) != mult(a(), mult(b(), mult(d(), c())))
% 8.61/8.90 To show the unsatisfiability of the original goal,
% 8.61/8.90 it suffices to show that mult(a(), mult(b(), mult(a(), mult(c(), mult(d(), c()))))) = mult(a(), mult(b(), mult(d(), c()))) (skolemized goal) is valid under the axioms.
% 8.61/8.90 Here is an equational proof:
% 8.61/8.90 0: mult(X0, mult(X1, mult(X0, X1))) = mult(X0, X1).
% 8.61/8.90 Proof: Axiom.
% 8.61/8.90
% 8.61/8.90 1: mult(X0, mult(X1, mult(X2, X3))) = mult(X2, mult(X1, mult(X0, X3))).
% 8.61/8.90 Proof: Axiom.
% 8.61/8.90
% 8.61/8.90 2: mult(mult(X0, mult(X1, mult(X2, X1))), X3) = mult(X0, mult(X3, mult(mult(X2, X1), X3))).
% 8.61/8.90 Proof: Axiom.
% 8.61/8.90
% 8.61/8.90 8: mult(mult(X6, X7), mult(X5, mult(X4, X5))) = mult(mult(X4, mult(X7, mult(X6, X7))), X5).
% 8.61/8.90 Proof: A critical pair between equations 1 and 2.
% 8.61/8.90
% 8.61/8.90 9: mult(X4, mult(X1, mult(X2, mult(X5, mult(X4, X5))))) = mult(X2, mult(X1, mult(X4, X5))).
% 8.61/8.90 Proof: A critical pair between equations 1 and 0.
% 8.61/8.90
% 8.61/8.90 12: mult(X4, mult(X1, mult(X2, mult(X5, mult(X6, X7))))) = mult(X2, mult(X1, mult(X6, mult(X5, mult(X4, X7))))).
% 8.61/8.90 Proof: A critical pair between equations 1 and 1.
% 8.61/8.90
% 8.61/8.90 18: mult(mult(X8, X9), mult(X5, mult(X8, X5))) = mult(mult(X8, X9), X5).
% 8.61/8.90 Proof: A critical pair between equations 8 and 0.
% 8.61/8.90
% 8.61/8.90 20: mult(mult(X4, X6), mult(X6, mult(X4, X6))) = mult(X4, mult(X6, mult(X4, X6))).
% 8.61/8.90 Proof: A critical pair between equations 9 and 0.
% 8.61/8.90
% 8.61/8.90 23: mult(X8, mult(X9, mult(X8, mult(X11, mult(X10, X11))))) = mult(X10, mult(X9, mult(X8, X11))).
% 8.61/8.90 Proof: A critical pair between equations 12 and 9.
% 8.61/8.90
% 8.61/8.90 29: mult(mult(X4, X6), X6) = mult(X4, X6).
% 8.61/8.90 Proof: Rewrite equation 20,
% 8.61/8.90 lhs with equations [18]
% 8.61/8.90 rhs with equations [0].
% 8.61/8.90
% 8.61/8.90 34: mult(mult(X7, X8), mult(X1, mult(X2, X8))) = mult(X2, mult(X1, mult(X7, X8))).
% 8.61/8.90 Proof: A critical pair between equations 1 and 29.
% 8.61/8.90
% 8.61/8.90 48: mult(mult(X11, X12), mult(X10, mult(X9, X12))) = mult(X11, mult(X10, mult(X9, X12))).
% 8.61/8.90 Proof: A critical pair between equations 34 and 1.
% 8.61/8.90
% 8.61/8.90 56: mult(mult(mult(X9, X10), X10), mult(X1, mult(X2, X10))) = mult(X2, mult(X1, mult(X9, X10))).
% 8.61/8.90 Proof: A critical pair between equations 34 and 29.
% 8.61/8.90
% 8.61/8.90 57: mult(X9, mult(X1, mult(X2, X10))) = mult(X2, mult(X1, mult(X9, X10))).
% 8.61/8.90 Proof: Rewrite equation 56,
% 8.61/8.90 lhs with equations [29,48]
% 8.61/8.90 rhs with equations [].
% 8.61/8.90
% 8.61/8.90 73: mult(X14, mult(X13, mult(X12, X15))) = mult(X14, mult(X13, mult(X14, mult(X15, mult(X12, X15))))).
% 8.61/8.90 Proof: A critical pair between equations 57 and 23.
% 8.61/8.90
% 8.61/8.90 86: mult(a(), mult(b(), mult(a(), mult(c(), mult(d(), c()))))) = mult(a(), mult(b(), mult(d(), c()))).
% 8.61/8.90 Proof: Rewrite lhs with equations [73]
% 8.61/8.90 rhs with equations [].
% 8.61/8.90
% 8.61/8.90 % SZS output end Proof
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