TSTP Solution File: GRP699-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP699-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n032.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 : Thu Aug 31 01:16:04 EDT 2023
% Result : Unsatisfiable 2.83s 3.12s
% Output : CNFRefutation 2.83s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP699-1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.12 % Command : toma --casc %s
% 0.12/0.32 % Computer : n032.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue Aug 29 01:48:46 EDT 2023
% 0.12/0.32 % CPUTime :
% 2.83/3.12 % SZS status Unsatisfiable
% 2.83/3.12 % SZS output start Proof
% 2.83/3.12 original problem:
% 2.83/3.12 axioms:
% 2.83/3.12 mult(A, ld(A, B)) = B
% 2.83/3.12 ld(A, mult(A, B)) = B
% 2.83/3.12 mult(rd(A, B), B) = A
% 2.83/3.12 rd(mult(A, B), B) = A
% 2.83/3.12 mult(A, unit()) = A
% 2.83/3.12 mult(unit(), A) = A
% 2.83/3.12 mult(mult(mult(A, B), A), mult(A, C)) = mult(A, mult(mult(mult(B, A), A), C))
% 2.83/3.12 mult(mult(A, B), mult(B, mult(C, B))) = mult(mult(A, mult(B, mult(B, C))), B)
% 2.83/3.12 goal:
% 2.83/3.12 mult(mult(a(), b()), c()) != mult(mult(a(), c()), ld(c(), mult(b(), c())))
% 2.83/3.12 To show the unsatisfiability of the original goal,
% 2.83/3.12 it suffices to show that mult(mult(a(), b()), c()) = mult(mult(a(), c()), ld(c(), mult(b(), c()))) (skolemized goal) is valid under the axioms.
% 2.83/3.12 Here is an equational proof:
% 2.83/3.12 0: mult(X0, ld(X0, X1)) = X1.
% 2.83/3.12 Proof: Axiom.
% 2.83/3.12
% 2.83/3.12 1: ld(X0, mult(X0, X1)) = X1.
% 2.83/3.12 Proof: Axiom.
% 2.83/3.12
% 2.83/3.12 5: mult(unit(), X0) = X0.
% 2.83/3.12 Proof: Axiom.
% 2.83/3.12
% 2.83/3.12 7: mult(mult(X0, X1), mult(X1, mult(X2, X1))) = mult(mult(X0, mult(X1, mult(X1, X2))), X1).
% 2.83/3.12 Proof: Axiom.
% 2.83/3.12
% 2.83/3.12 19: mult(mult(unit(), X1), mult(X1, mult(X2, X1))) = mult(mult(X1, mult(X1, X2)), X1).
% 2.83/3.12 Proof: A critical pair between equations 7 and 5.
% 2.83/3.12
% 2.83/3.12 23: mult(X1, mult(X1, mult(X2, X1))) = mult(mult(X1, mult(X1, X2)), X1).
% 2.83/3.12 Proof: Rewrite equation 19,
% 2.83/3.12 lhs with equations [5]
% 2.83/3.12 rhs with equations [].
% 2.83/3.12
% 2.83/3.12 71: mult(X3, mult(X3, mult(ld(X3, X4), X3))) = mult(mult(X3, X4), X3).
% 2.83/3.12 Proof: A critical pair between equations 23 and 0.
% 2.83/3.12
% 2.83/3.12 80: mult(X5, mult(X5, mult(ld(X5, ld(X5, X6)), X5))) = mult(X6, X5).
% 2.83/3.12 Proof: A critical pair between equations 71 and 0.
% 2.83/3.12
% 2.83/3.12 98: mult(X7, mult(ld(X7, ld(X7, X8)), X7)) = ld(X7, mult(X8, X7)).
% 2.83/3.12 Proof: A critical pair between equations 1 and 80.
% 2.83/3.12
% 2.83/3.12 179: mult(ld(X9, ld(X9, X10)), X9) = ld(X9, ld(X9, mult(X10, X9))).
% 2.83/3.12 Proof: A critical pair between equations 1 and 98.
% 2.83/3.12
% 2.83/3.12 279: mult(mult(X0, X3), mult(X3, mult(ld(X3, X4), X3))) = mult(mult(X0, mult(X3, X4)), X3).
% 2.83/3.12 Proof: A critical pair between equations 7 and 0.
% 2.83/3.12
% 2.83/3.12 295: mult(mult(X0, X5), mult(X5, mult(ld(X5, ld(X5, X6)), X5))) = mult(mult(X0, X6), X5).
% 2.83/3.12 Proof: A critical pair between equations 279 and 0.
% 2.83/3.12
% 2.83/3.12 299: mult(mult(X0, X5), ld(X5, mult(X6, X5))) = mult(mult(X0, X6), X5).
% 2.83/3.12 Proof: Rewrite equation 295,
% 2.83/3.12 lhs with equations [179,0]
% 2.83/3.12 rhs with equations [].
% 2.83/3.12
% 2.83/3.12 301: mult(mult(a(), b()), c()) = mult(mult(a(), c()), ld(c(), mult(b(), c()))).
% 2.83/3.12 Proof: Rewrite lhs with equations []
% 2.83/3.12 rhs with equations [299].
% 2.83/3.12
% 2.83/3.12 % SZS output end Proof
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