TSTP Solution File: GRP704-12 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP704-12 : TPTP v8.1.2. Released v8.1.0.
% 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 : n027.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 01:19:49 EDT 2023
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP704-12 : TPTP v8.1.2. Released v8.1.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n027.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
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 29 00:27:22 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.21/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.39
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 Axiom 1 (f05): mult(X, unit) = X.
% 0.21/0.40 Axiom 2 (f06): mult(unit, X) = X.
% 0.21/0.40 Axiom 3 (f02): ld(X, mult(X, Y)) = Y.
% 0.21/0.40 Axiom 4 (f11): op_d = ld(X, mult(op_c, X)).
% 0.21/0.40 Axiom 5 (f01): mult(X, ld(X, Y)) = Y.
% 0.21/0.40 Axiom 6 (f09): mult(X, mult(Y, op_c)) = mult(mult(X, Y), op_c).
% 0.21/0.40 Axiom 7 (f08): mult(op_c, mult(X, Y)) = mult(mult(op_c, X), Y).
% 0.21/0.40 Axiom 8 (f13): op_f = mult(X, mult(Y, ld(mult(X, Y), op_c))).
% 0.21/0.40
% 0.21/0.40 Lemma 9: op_c = op_d.
% 0.21/0.40 Proof:
% 0.21/0.40 op_c
% 0.21/0.40 = { by axiom 3 (f02) R->L }
% 0.21/0.40 ld(op_c, mult(op_c, op_c))
% 0.21/0.40 = { by axiom 4 (f11) R->L }
% 0.21/0.40 op_d
% 0.21/0.40
% 0.21/0.40 Lemma 10: op_f = op_d.
% 0.21/0.40 Proof:
% 0.21/0.40 op_f
% 0.21/0.40 = { by axiom 8 (f13) }
% 0.21/0.40 mult(X, mult(unit, ld(mult(X, unit), op_c)))
% 0.21/0.40 = { by axiom 1 (f05) }
% 0.21/0.40 mult(X, mult(unit, ld(X, op_c)))
% 0.21/0.40 = { by axiom 2 (f06) }
% 0.21/0.40 mult(X, ld(X, op_c))
% 0.21/0.40 = { by axiom 5 (f01) }
% 0.21/0.40 op_c
% 0.21/0.40 = { by lemma 9 }
% 0.21/0.40 op_d
% 0.21/0.40
% 0.21/0.40 Lemma 11: mult(op_d, X) = mult(X, op_d).
% 0.21/0.40 Proof:
% 0.21/0.40 mult(op_d, X)
% 0.21/0.40 = { by lemma 9 R->L }
% 0.21/0.40 mult(op_c, X)
% 0.21/0.40 = { by axiom 5 (f01) R->L }
% 0.21/0.40 mult(X, ld(X, mult(op_c, X)))
% 0.21/0.40 = { by axiom 4 (f11) R->L }
% 0.21/0.40 mult(X, op_d)
% 0.21/0.40
% 0.21/0.40 Goal 1 (goal): mult(x4, mult(op_f, x5)) = mult(mult(x4, op_f), x5).
% 0.21/0.40 Proof:
% 0.21/0.40 mult(x4, mult(op_f, x5))
% 0.21/0.40 = { by lemma 10 }
% 0.21/0.40 mult(x4, mult(op_d, x5))
% 0.21/0.40 = { by lemma 11 }
% 0.21/0.40 mult(x4, mult(x5, op_d))
% 0.21/0.40 = { by lemma 9 R->L }
% 0.21/0.40 mult(x4, mult(x5, op_c))
% 0.21/0.40 = { by axiom 6 (f09) }
% 0.21/0.40 mult(mult(x4, x5), op_c)
% 0.21/0.40 = { by lemma 9 }
% 0.21/0.40 mult(mult(x4, x5), op_d)
% 0.21/0.40 = { by lemma 11 R->L }
% 0.21/0.40 mult(op_d, mult(x4, x5))
% 0.21/0.40 = { by lemma 9 R->L }
% 0.21/0.40 mult(op_c, mult(x4, x5))
% 0.21/0.40 = { by axiom 7 (f08) }
% 0.21/0.40 mult(mult(op_c, x4), x5)
% 0.21/0.40 = { by lemma 9 }
% 0.21/0.40 mult(mult(op_d, x4), x5)
% 0.21/0.40 = { by lemma 11 }
% 0.21/0.40 mult(mult(x4, op_d), x5)
% 0.21/0.40 = { by lemma 10 R->L }
% 0.21/0.40 mult(mult(x4, op_f), x5)
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40
% 0.21/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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