TSTP Solution File: GRP681-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP681-1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 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 01:19:40 EDT 2023
% Result : Unsatisfiable 4.82s 1.00s
% Output : Proof 4.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP681-1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.32 % Computer : n023.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 : Mon Aug 28 23:11:40 EDT 2023
% 0.12/0.32 % CPUTime :
% 4.82/1.00 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 4.82/1.00
% 4.82/1.00 % SZS status Unsatisfiable
% 4.82/1.00
% 4.82/1.02 % SZS output start Proof
% 4.82/1.02 Axiom 1 (c08): mult(op_c, X) = mult(X, op_c).
% 4.82/1.02 Axiom 2 (c09): mult(op_d, X) = mult(X, op_d).
% 4.82/1.02 Axiom 3 (c06): mult(unit, X) = X.
% 4.82/1.02 Axiom 4 (c02): ld(X, mult(X, Y)) = Y.
% 4.82/1.02 Axiom 5 (c07): mult(X, mult(Y, mult(X, Z))) = mult(mult(X, mult(Y, X)), Z).
% 4.82/1.02
% 4.82/1.02 Lemma 6: mult(mult(X, X), Y) = mult(X, mult(X, Y)).
% 4.82/1.02 Proof:
% 4.82/1.02 mult(mult(X, X), Y)
% 4.82/1.02 = { by axiom 3 (c06) R->L }
% 4.82/1.02 mult(mult(X, mult(unit, X)), Y)
% 4.82/1.02 = { by axiom 5 (c07) R->L }
% 4.82/1.02 mult(X, mult(unit, mult(X, Y)))
% 4.82/1.02 = { by axiom 3 (c06) }
% 4.82/1.02 mult(X, mult(X, Y))
% 4.82/1.02
% 4.82/1.02 Lemma 7: mult(mult(op_c, op_c), X) = mult(op_c, mult(X, op_c)).
% 4.82/1.02 Proof:
% 4.82/1.02 mult(mult(op_c, op_c), X)
% 4.82/1.02 = { by lemma 6 }
% 4.82/1.02 mult(op_c, mult(op_c, X))
% 4.82/1.02 = { by axiom 1 (c08) }
% 4.82/1.02 mult(op_c, mult(X, op_c))
% 4.82/1.02
% 4.82/1.02 Lemma 8: mult(op_c, mult(X, mult(Y, X))) = mult(X, mult(Y, mult(X, op_c))).
% 4.82/1.02 Proof:
% 4.82/1.02 mult(op_c, mult(X, mult(Y, X)))
% 4.82/1.02 = { by axiom 1 (c08) }
% 4.82/1.02 mult(mult(X, mult(Y, X)), op_c)
% 4.82/1.02 = { by axiom 5 (c07) R->L }
% 4.82/1.02 mult(X, mult(Y, mult(X, op_c)))
% 4.82/1.02
% 4.82/1.02 Lemma 9: mult(mult(op_c, op_c), X) = mult(X, mult(op_c, op_c)).
% 4.82/1.02 Proof:
% 4.82/1.02 mult(mult(op_c, op_c), X)
% 4.82/1.02 = { by axiom 4 (c02) R->L }
% 4.82/1.02 ld(op_c, mult(op_c, mult(mult(op_c, op_c), X)))
% 4.82/1.02 = { by lemma 7 }
% 4.82/1.02 ld(op_c, mult(op_c, mult(op_c, mult(X, op_c))))
% 4.82/1.02 = { by lemma 8 }
% 4.82/1.02 ld(op_c, mult(op_c, mult(X, mult(op_c, op_c))))
% 4.82/1.02 = { by axiom 4 (c02) }
% 4.82/1.02 mult(X, mult(op_c, op_c))
% 4.82/1.02
% 4.82/1.02 Lemma 10: mult(mult(X, mult(op_c, op_c)), Y) = mult(op_c, mult(X, mult(op_c, Y))).
% 4.82/1.02 Proof:
% 4.82/1.02 mult(mult(X, mult(op_c, op_c)), Y)
% 4.82/1.02 = { by lemma 9 R->L }
% 4.82/1.02 mult(mult(mult(op_c, op_c), X), Y)
% 4.82/1.02 = { by lemma 6 }
% 4.82/1.02 mult(mult(op_c, mult(op_c, X)), Y)
% 4.82/1.02 = { by axiom 1 (c08) }
% 4.82/1.02 mult(mult(op_c, mult(X, op_c)), Y)
% 4.82/1.02 = { by axiom 5 (c07) R->L }
% 4.82/1.02 mult(op_c, mult(X, mult(op_c, Y)))
% 4.82/1.02
% 4.82/1.02 Goal 1 (goals): mult(mult(mult(op_c, op_c), op_d), a) = mult(a, mult(mult(op_c, op_c), op_d)).
% 4.82/1.02 Proof:
% 4.82/1.02 mult(mult(mult(op_c, op_c), op_d), a)
% 4.82/1.02 = { by axiom 4 (c02) R->L }
% 4.82/1.02 ld(a, mult(a, mult(mult(mult(op_c, op_c), op_d), a)))
% 4.82/1.02 = { by axiom 4 (c02) R->L }
% 4.82/1.02 ld(a, ld(op_c, mult(op_c, mult(a, mult(mult(mult(op_c, op_c), op_d), a)))))
% 4.82/1.02 = { by axiom 1 (c08) }
% 4.82/1.02 ld(a, ld(op_c, mult(mult(a, mult(mult(mult(op_c, op_c), op_d), a)), op_c)))
% 4.82/1.02 = { by axiom 5 (c07) R->L }
% 4.82/1.02 ld(a, ld(op_c, mult(a, mult(mult(mult(op_c, op_c), op_d), mult(a, op_c)))))
% 4.82/1.02 = { by axiom 2 (c09) R->L }
% 4.82/1.02 ld(a, ld(op_c, mult(a, mult(mult(op_d, mult(op_c, op_c)), mult(a, op_c)))))
% 4.82/1.02 = { by lemma 10 }
% 4.82/1.02 ld(a, ld(op_c, mult(a, mult(op_c, mult(op_d, mult(op_c, mult(a, op_c)))))))
% 4.82/1.02 = { by axiom 2 (c09) }
% 4.82/1.02 ld(a, ld(op_c, mult(a, mult(op_c, mult(mult(op_c, mult(a, op_c)), op_d)))))
% 4.82/1.02 = { by axiom 5 (c07) R->L }
% 4.82/1.02 ld(a, ld(op_c, mult(a, mult(op_c, mult(op_c, mult(a, mult(op_c, op_d)))))))
% 4.82/1.02 = { by lemma 6 R->L }
% 4.82/1.02 ld(a, ld(op_c, mult(a, mult(mult(op_c, op_c), mult(a, mult(op_c, op_d))))))
% 4.82/1.02 = { by axiom 5 (c07) }
% 4.82/1.02 ld(a, ld(op_c, mult(mult(a, mult(mult(op_c, op_c), a)), mult(op_c, op_d))))
% 4.82/1.02 = { by lemma 7 }
% 4.82/1.02 ld(a, ld(op_c, mult(mult(a, mult(op_c, mult(a, op_c))), mult(op_c, op_d))))
% 4.82/1.02 = { by lemma 8 R->L }
% 4.82/1.02 ld(a, ld(op_c, mult(mult(op_c, mult(a, mult(op_c, a))), mult(op_c, op_d))))
% 4.82/1.02 = { by axiom 1 (c08) }
% 4.82/1.02 ld(a, ld(op_c, mult(mult(op_c, mult(a, mult(a, op_c))), mult(op_c, op_d))))
% 4.82/1.02 = { by lemma 6 R->L }
% 4.82/1.02 ld(a, ld(op_c, mult(mult(op_c, mult(mult(a, a), op_c)), mult(op_c, op_d))))
% 4.82/1.02 = { by axiom 1 (c08) R->L }
% 4.82/1.02 ld(a, ld(op_c, mult(mult(op_c, mult(op_c, mult(a, a))), mult(op_c, op_d))))
% 4.82/1.02 = { by lemma 6 R->L }
% 4.82/1.02 ld(a, ld(op_c, mult(mult(mult(op_c, op_c), mult(a, a)), mult(op_c, op_d))))
% 4.82/1.02 = { by lemma 9 }
% 4.82/1.02 ld(a, ld(op_c, mult(mult(mult(a, a), mult(op_c, op_c)), mult(op_c, op_d))))
% 4.82/1.02 = { by lemma 10 }
% 4.82/1.02 ld(a, ld(op_c, mult(op_c, mult(mult(a, a), mult(op_c, mult(op_c, op_d))))))
% 4.82/1.02 = { by lemma 6 R->L }
% 4.82/1.02 ld(a, ld(op_c, mult(op_c, mult(mult(a, a), mult(mult(op_c, op_c), op_d)))))
% 4.82/1.02 = { by lemma 6 }
% 4.82/1.02 ld(a, ld(op_c, mult(op_c, mult(a, mult(a, mult(mult(op_c, op_c), op_d))))))
% 4.82/1.02 = { by axiom 4 (c02) }
% 4.82/1.02 ld(a, mult(a, mult(a, mult(mult(op_c, op_c), op_d))))
% 4.82/1.02 = { by axiom 4 (c02) }
% 4.82/1.02 mult(a, mult(mult(op_c, op_c), op_d))
% 4.82/1.02 % SZS output end Proof
% 4.82/1.02
% 4.82/1.02 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------