TSTP Solution File: GRP686-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP686-1 : 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 : n011.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 0.44s
% 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
% 0.12/0.12 % Problem : GRP686-1 : 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 : n011.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 22:32:41 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.44 Command-line arguments: --no-flatten-goal
% 0.20/0.44
% 0.20/0.44 % SZS status Unsatisfiable
% 0.20/0.44
% 0.20/0.45 % SZS output start Proof
% 0.20/0.45 Axiom 1 (c05): mult(X, unit) = X.
% 0.20/0.45 Axiom 2 (c06): mult(unit, X) = X.
% 0.20/0.45 Axiom 3 (c02): ld(X, mult(X, Y)) = Y.
% 0.20/0.45 Axiom 4 (c04): rd(mult(X, Y), Y) = X.
% 0.20/0.45 Axiom 5 (c01): mult(X, ld(X, Y)) = Y.
% 0.20/0.45 Axiom 6 (c03): mult(rd(X, Y), Y) = X.
% 0.20/0.45 Axiom 7 (c07): mult(X, mult(Y, mult(Y, Z))) = mult(mult(X, mult(Y, Y)), Z).
% 0.20/0.45
% 0.20/0.45 Lemma 8: rd(X, ld(Y, X)) = Y.
% 0.20/0.45 Proof:
% 0.20/0.45 rd(X, ld(Y, X))
% 0.20/0.45 = { by axiom 5 (c01) R->L }
% 0.20/0.45 rd(mult(Y, ld(Y, X)), ld(Y, X))
% 0.20/0.45 = { by axiom 4 (c04) }
% 0.20/0.45 Y
% 0.20/0.45
% 0.20/0.45 Lemma 9: mult(rd(X, mult(Y, Y)), mult(Y, mult(Y, Z))) = mult(X, Z).
% 0.20/0.45 Proof:
% 0.20/0.45 mult(rd(X, mult(Y, Y)), mult(Y, mult(Y, Z)))
% 0.20/0.45 = { by axiom 7 (c07) }
% 0.20/0.45 mult(mult(rd(X, mult(Y, Y)), mult(Y, Y)), Z)
% 0.20/0.46 = { by axiom 6 (c03) }
% 0.20/0.46 mult(X, Z)
% 0.20/0.46
% 0.20/0.46 Lemma 10: ld(rd(X, mult(Y, Y)), mult(X, Z)) = mult(Y, mult(Y, Z)).
% 0.20/0.46 Proof:
% 0.20/0.46 ld(rd(X, mult(Y, Y)), mult(X, Z))
% 0.20/0.46 = { by lemma 9 R->L }
% 0.20/0.46 ld(rd(X, mult(Y, Y)), mult(rd(X, mult(Y, Y)), mult(Y, mult(Y, Z))))
% 0.20/0.46 = { by axiom 3 (c02) }
% 0.20/0.46 mult(Y, mult(Y, Z))
% 0.20/0.46
% 0.20/0.46 Lemma 11: ld(ld(X, unit), Y) = mult(X, Y).
% 0.20/0.46 Proof:
% 0.20/0.46 ld(ld(X, unit), Y)
% 0.20/0.46 = { by axiom 4 (c04) R->L }
% 0.20/0.46 ld(rd(mult(ld(X, unit), mult(X, X)), mult(X, X)), Y)
% 0.20/0.46 = { by axiom 4 (c04) R->L }
% 0.20/0.46 ld(rd(rd(mult(mult(ld(X, unit), mult(X, X)), ld(X, ld(X, unit))), ld(X, ld(X, unit))), mult(X, X)), Y)
% 0.20/0.46 = { by axiom 7 (c07) R->L }
% 0.20/0.46 ld(rd(rd(mult(ld(X, unit), mult(X, mult(X, ld(X, ld(X, unit))))), ld(X, ld(X, unit))), mult(X, X)), Y)
% 0.20/0.46 = { by axiom 5 (c01) }
% 0.20/0.46 ld(rd(rd(mult(ld(X, unit), mult(X, ld(X, unit))), ld(X, ld(X, unit))), mult(X, X)), Y)
% 0.20/0.46 = { by axiom 5 (c01) }
% 0.20/0.46 ld(rd(rd(mult(ld(X, unit), unit), ld(X, ld(X, unit))), mult(X, X)), Y)
% 0.20/0.46 = { by axiom 1 (c05) }
% 0.20/0.46 ld(rd(rd(ld(X, unit), ld(X, ld(X, unit))), mult(X, X)), Y)
% 0.20/0.46 = { by lemma 8 }
% 0.20/0.46 ld(rd(X, mult(X, X)), Y)
% 0.20/0.46 = { by axiom 5 (c01) R->L }
% 0.20/0.46 ld(rd(X, mult(X, X)), mult(X, ld(X, Y)))
% 0.20/0.46 = { by lemma 10 }
% 0.20/0.46 mult(X, mult(X, ld(X, Y)))
% 0.20/0.46 = { by axiom 5 (c01) }
% 0.20/0.46 mult(X, Y)
% 0.20/0.46
% 0.20/0.46 Goal 1 (goals): mult(mult(a, a), mult(b, c)) = mult(mult(a, mult(a, b)), c).
% 0.20/0.46 Proof:
% 0.20/0.46 mult(mult(a, a), mult(b, c))
% 0.20/0.46 = { by axiom 2 (c06) R->L }
% 0.20/0.46 mult(mult(unit, mult(a, a)), mult(b, c))
% 0.20/0.46 = { by axiom 7 (c07) R->L }
% 0.20/0.46 mult(unit, mult(a, mult(a, mult(b, c))))
% 0.20/0.46 = { by axiom 2 (c06) }
% 0.20/0.46 mult(a, mult(a, mult(b, c)))
% 0.20/0.46 = { by lemma 10 R->L }
% 0.20/0.46 ld(rd(b, mult(a, a)), mult(b, mult(b, c)))
% 0.20/0.46 = { by lemma 8 R->L }
% 0.20/0.46 ld(rd(mult(b, b), ld(rd(b, mult(a, a)), mult(b, b))), mult(b, mult(b, c)))
% 0.20/0.46 = { by axiom 6 (c03) R->L }
% 0.20/0.46 ld(rd(mult(b, b), mult(rd(ld(rd(b, mult(a, a)), mult(b, b)), mult(b, b)), mult(b, b))), mult(b, mult(b, c)))
% 0.20/0.46 = { by lemma 11 R->L }
% 0.20/0.46 ld(rd(mult(b, b), ld(ld(rd(ld(rd(b, mult(a, a)), mult(b, b)), mult(b, b)), unit), mult(b, b))), mult(b, mult(b, c)))
% 0.20/0.46 = { by lemma 8 }
% 0.20/0.46 ld(ld(rd(ld(rd(b, mult(a, a)), mult(b, b)), mult(b, b)), unit), mult(b, mult(b, c)))
% 0.20/0.46 = { by lemma 11 }
% 0.20/0.46 mult(rd(ld(rd(b, mult(a, a)), mult(b, b)), mult(b, b)), mult(b, mult(b, c)))
% 0.20/0.46 = { by axiom 5 (c01) R->L }
% 0.20/0.46 mult(rd(ld(rd(b, mult(a, a)), mult(b, b)), mult(b, b)), mult(b, mult(b, ld(b, mult(b, c)))))
% 0.20/0.46 = { by lemma 9 }
% 0.20/0.46 mult(ld(rd(b, mult(a, a)), mult(b, b)), ld(b, mult(b, c)))
% 0.20/0.46 = { by axiom 3 (c02) }
% 0.20/0.46 mult(ld(rd(b, mult(a, a)), mult(b, b)), c)
% 0.20/0.46 = { by lemma 10 }
% 0.20/0.46 mult(mult(a, mult(a, b)), c)
% 0.20/0.46 % SZS output end Proof
% 0.20/0.46
% 0.20/0.46 RESULT: Unsatisfiable (the axioms are contradictory).
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