TSTP Solution File: GRP687-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP687-1 : 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 : 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 01:19:43 EDT 2023
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% 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 : GRP687-1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 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
% 0.20/0.34 % DateTime : Mon Aug 28 21:16:20 EDT 2023
% 0.20/0.34 % CPUTime :
% 0.20/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.20/0.39
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39
% 0.20/0.40 % SZS output start Proof
% 0.20/0.40 Axiom 1 (c05): mult(X, unit) = X.
% 0.20/0.40 Axiom 2 (c02): ld(X, mult(X, Y)) = Y.
% 0.20/0.40 Axiom 3 (c01): mult(X, ld(X, Y)) = Y.
% 0.20/0.40 Axiom 4 (c07): mult(mult(X, X), mult(Y, Z)) = mult(mult(X, mult(X, Y)), Z).
% 0.20/0.40
% 0.20/0.40 Lemma 5: mult(mult(X, X), Y) = mult(X, mult(X, Y)).
% 0.20/0.40 Proof:
% 0.20/0.40 mult(mult(X, X), Y)
% 0.20/0.40 = { by axiom 1 (c05) R->L }
% 0.20/0.40 mult(mult(X, X), mult(Y, unit))
% 0.20/0.40 = { by axiom 4 (c07) }
% 0.20/0.40 mult(mult(X, mult(X, Y)), unit)
% 0.20/0.40 = { by axiom 1 (c05) }
% 0.20/0.40 mult(X, mult(X, Y))
% 0.20/0.40
% 0.20/0.40 Lemma 6: mult(X, mult(ld(X, Y), Z)) = ld(X, mult(mult(X, Y), Z)).
% 0.20/0.40 Proof:
% 0.20/0.40 mult(X, mult(ld(X, Y), Z))
% 0.20/0.40 = { by axiom 2 (c02) R->L }
% 0.20/0.40 ld(X, mult(X, mult(X, mult(ld(X, Y), Z))))
% 0.20/0.40 = { by lemma 5 R->L }
% 0.20/0.40 ld(X, mult(mult(X, X), mult(ld(X, Y), Z)))
% 0.20/0.40 = { by axiom 4 (c07) }
% 0.20/0.40 ld(X, mult(mult(X, mult(X, ld(X, Y))), Z))
% 0.20/0.40 = { by axiom 3 (c01) }
% 0.20/0.40 ld(X, mult(mult(X, Y), Z))
% 0.20/0.40
% 0.20/0.40 Lemma 7: ld(mult(X, mult(X, Y)), mult(X, mult(X, Z))) = ld(Y, Z).
% 0.20/0.40 Proof:
% 0.20/0.40 ld(mult(X, mult(X, Y)), mult(X, mult(X, Z)))
% 0.20/0.40 = { by axiom 3 (c01) R->L }
% 0.20/0.40 ld(mult(X, mult(X, Y)), mult(X, mult(X, mult(Y, ld(Y, Z)))))
% 0.20/0.40 = { by lemma 5 R->L }
% 0.20/0.40 ld(mult(X, mult(X, Y)), mult(mult(X, X), mult(Y, ld(Y, Z))))
% 0.20/0.40 = { by axiom 4 (c07) }
% 0.20/0.40 ld(mult(X, mult(X, Y)), mult(mult(X, mult(X, Y)), ld(Y, Z)))
% 0.20/0.40 = { by axiom 2 (c02) }
% 0.20/0.40 ld(Y, Z)
% 0.20/0.40
% 0.20/0.40 Goal 1 (goals): mult(a, mult(b, mult(b, c))) = mult(mult(a, mult(b, b)), c).
% 0.20/0.40 Proof:
% 0.20/0.40 mult(a, mult(b, mult(b, c)))
% 0.20/0.41 = { by axiom 2 (c02) R->L }
% 0.20/0.41 mult(a, mult(b, mult(b, ld(a, mult(a, c)))))
% 0.20/0.41 = { by axiom 1 (c05) R->L }
% 0.20/0.41 mult(a, mult(b, mult(b, ld(a, mult(mult(a, unit), c)))))
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 mult(a, mult(b, mult(b, mult(a, mult(ld(a, unit), c)))))
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 mult(a, mult(mult(b, b), mult(a, mult(ld(a, unit), c))))
% 0.20/0.41 = { by axiom 4 (c07) }
% 0.20/0.41 mult(a, mult(mult(b, mult(b, a)), mult(ld(a, unit), c)))
% 0.20/0.41 = { by lemma 7 R->L }
% 0.20/0.41 mult(a, mult(mult(b, mult(b, a)), mult(ld(mult(b, mult(b, a)), mult(b, mult(b, unit))), c)))
% 0.20/0.41 = { by axiom 1 (c05) }
% 0.20/0.41 mult(a, mult(mult(b, mult(b, a)), mult(ld(mult(b, mult(b, a)), mult(b, b)), c)))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 mult(a, ld(mult(b, mult(b, a)), mult(mult(mult(b, mult(b, a)), mult(b, b)), c)))
% 0.20/0.41 = { by axiom 4 (c07) R->L }
% 0.20/0.41 mult(a, ld(mult(b, mult(b, a)), mult(mult(mult(b, b), mult(a, mult(b, b))), c)))
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 mult(a, ld(mult(b, mult(b, a)), mult(mult(b, mult(b, mult(a, mult(b, b)))), c)))
% 0.20/0.41 = { by axiom 4 (c07) R->L }
% 0.20/0.41 mult(a, ld(mult(b, mult(b, a)), mult(mult(b, b), mult(mult(a, mult(b, b)), c))))
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 mult(a, ld(mult(b, mult(b, a)), mult(b, mult(b, mult(mult(a, mult(b, b)), c)))))
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 mult(a, ld(a, mult(mult(a, mult(b, b)), c)))
% 0.20/0.41 = { by axiom 3 (c01) }
% 0.20/0.41 mult(mult(a, mult(b, b)), c)
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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