TSTP Solution File: GRP679-1 by Toma---0.4
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% File : Toma---0.4
% Problem : GRP679-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n009.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 01:16:00 EDT 2023
% Result : Unsatisfiable 0.52s 0.87s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP679-1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n009.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 23:06:05 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.52/0.87 % SZS status Unsatisfiable
% 0.52/0.87 % SZS output start Proof
% 0.52/0.87 original problem:
% 0.52/0.87 axioms:
% 0.52/0.87 mult(A, ld(A, B)) = B
% 0.52/0.87 ld(A, mult(A, B)) = B
% 0.52/0.87 mult(rd(A, B), B) = A
% 0.52/0.87 rd(mult(A, B), B) = A
% 0.52/0.87 mult(A, unit()) = A
% 0.52/0.87 mult(unit(), A) = A
% 0.52/0.87 mult(A, mult(B, mult(A, C))) = mult(mult(A, mult(B, A)), C)
% 0.52/0.87 mult(op_c(), A) = mult(A, op_c())
% 0.52/0.87 goal:
% 0.52/0.87 mult(mult(op_c(), op_c()), a()) != mult(a(), mult(op_c(), op_c()))
% 0.52/0.87 To show the unsatisfiability of the original goal,
% 0.52/0.87 it suffices to show that mult(mult(op_c(), op_c()), a()) = mult(a(), mult(op_c(), op_c())) (skolemized goal) is valid under the axioms.
% 0.52/0.87 Here is an equational proof:
% 0.52/0.87 0: mult(X0, ld(X0, X1)) = X1.
% 0.52/0.87 Proof: Axiom.
% 0.52/0.87
% 0.52/0.87 1: ld(X0, mult(X0, X1)) = X1.
% 0.52/0.87 Proof: Axiom.
% 0.52/0.87
% 0.52/0.87 3: rd(mult(X0, X1), X1) = X0.
% 0.52/0.87 Proof: Axiom.
% 0.52/0.87
% 0.52/0.87 5: mult(unit(), X0) = X0.
% 0.52/0.87 Proof: Axiom.
% 0.52/0.87
% 0.52/0.87 6: mult(X0, mult(X1, mult(X0, X2))) = mult(mult(X0, mult(X1, X0)), X2).
% 0.52/0.87 Proof: Axiom.
% 0.52/0.87
% 0.52/0.87 7: mult(op_c(), X0) = mult(X0, op_c()).
% 0.52/0.87 Proof: Axiom.
% 0.52/0.87
% 0.52/0.87 14: X2 = ld(op_c(), mult(X2, op_c())).
% 0.52/0.87 Proof: A critical pair between equations 1 and 7.
% 0.52/0.87
% 0.52/0.87 16: X2 = rd(mult(op_c(), X2), op_c()).
% 0.52/0.87 Proof: A critical pair between equations 3 and 7.
% 0.52/0.87
% 0.52/0.87 19: mult(X3, mult(unit(), mult(X3, X2))) = mult(mult(X3, X3), X2).
% 0.52/0.87 Proof: A critical pair between equations 6 and 5.
% 0.52/0.87
% 0.52/0.87 20: mult(X3, mult(X3, X2)) = mult(mult(X3, X3), X2).
% 0.52/0.87 Proof: Rewrite equation 19,
% 0.52/0.87 lhs with equations [5]
% 0.52/0.87 rhs with equations [].
% 0.52/0.87
% 0.52/0.87 22: ld(op_c(), X4) = rd(X4, op_c()).
% 0.52/0.87 Proof: A critical pair between equations 16 and 0.
% 0.52/0.87
% 0.52/0.87 32: mult(X3, mult(X4, X3)) = ld(op_c(), mult(X3, mult(X4, mult(X3, op_c())))).
% 0.52/0.87 Proof: A critical pair between equations 14 and 6.
% 0.52/0.87
% 0.52/0.87 33: mult(X3, mult(X4, X3)) = rd(mult(X3, mult(X4, mult(X3, op_c()))), op_c()).
% 0.52/0.87 Proof: Rewrite equation 32,
% 0.52/0.87 lhs with equations []
% 0.52/0.87 rhs with equations [22].
% 0.52/0.87
% 0.52/0.87 35: mult(op_c(), mult(X4, op_c())) = mult(X4, mult(op_c(), op_c())).
% 0.52/0.87 Proof: A critical pair between equations 33 and 16.
% 0.52/0.87
% 0.52/0.87 49: mult(mult(op_c(), op_c()), a()) = mult(a(), mult(op_c(), op_c())).
% 0.52/0.87 Proof: Rewrite lhs with equations [20]
% 0.52/0.87 rhs with equations [35,7].
% 0.52/0.87
% 0.52/0.87 % SZS output end Proof
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