TSTP Solution File: GRP665-12 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP665-12 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n023.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 01:15:56 EDT 2023
% Result : Unsatisfiable 0.53s 0.81s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : GRP665-12 : TPTP v8.1.2. Released v8.1.0.
% 0.12/0.13 % Command : toma --casc %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 23:02:10 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.53/0.81 % SZS status Unsatisfiable
% 0.53/0.81 % SZS output start Proof
% 0.53/0.81 original problem:
% 0.53/0.81 axioms:
% 0.53/0.81 mult(A, ld(A, B)) = B
% 0.53/0.81 ld(A, mult(A, B)) = B
% 0.53/0.81 mult(rd(A, B), B) = A
% 0.53/0.81 rd(mult(A, B), B) = A
% 0.53/0.81 mult(A, unit()) = A
% 0.53/0.81 mult(unit(), A) = A
% 0.53/0.81 mult(A, mult(B, C)) = mult(rd(mult(A, B), A), mult(A, C))
% 0.53/0.81 mult(mult(A, B), C) = mult(mult(A, C), ld(C, mult(B, C)))
% 0.53/0.81 mult(op_c(), A) = mult(A, op_c())
% 0.53/0.81 goal:
% 0.53/0.81 mult(mult(x0(), x1()), op_c()) != mult(x0(), mult(x1(), op_c()))
% 0.53/0.81 To show the unsatisfiability of the original goal,
% 0.53/0.81 it suffices to show that mult(mult(x0(), x1()), op_c()) = mult(x0(), mult(x1(), op_c())) (skolemized goal) is valid under the axioms.
% 0.53/0.81 Here is an equational proof:
% 0.53/0.81 3: rd(mult(X0, X1), X1) = X0.
% 0.53/0.81 Proof: Axiom.
% 0.53/0.81
% 0.53/0.81 6: mult(X0, mult(X1, X2)) = mult(rd(mult(X0, X1), X0), mult(X0, X2)).
% 0.53/0.81 Proof: Axiom.
% 0.53/0.81
% 0.53/0.81 8: mult(op_c(), X0) = mult(X0, op_c()).
% 0.53/0.81 Proof: Axiom.
% 0.53/0.81
% 0.53/0.81 18: op_c() = rd(mult(X2, op_c()), X2).
% 0.53/0.81 Proof: A critical pair between equations 3 and 8.
% 0.53/0.81
% 0.53/0.81 25: mult(X3, mult(op_c(), X2)) = mult(op_c(), mult(X3, X2)).
% 0.53/0.81 Proof: A critical pair between equations 6 and 18.
% 0.53/0.81
% 0.53/0.81 36: mult(mult(x0(), x1()), op_c()) = mult(x0(), mult(x1(), op_c())).
% 0.53/0.81 Proof: Rewrite lhs with equations [8]
% 0.53/0.81 rhs with equations [8,25].
% 0.53/0.81
% 0.53/0.81 % SZS output end Proof
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