TSTP Solution File: GRP697-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP697-1 : 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 : 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 01:19:45 EDT 2023
% Result : Unsatisfiable 0.19s 0.54s
% Output : Proof 0.19s
% 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 : GRP697-1 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.34 % Computer : n027.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 22:53:52 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.19/0.54 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.54
% 0.19/0.54 % SZS status Unsatisfiable
% 0.19/0.54
% 0.19/0.55 % SZS output start Proof
% 0.19/0.55 Axiom 1 (c05): mult(X, unit) = X.
% 0.19/0.55 Axiom 2 (c06): mult(unit, X) = X.
% 0.19/0.55 Axiom 3 (c11): mult(X, i(X)) = unit.
% 0.19/0.55 Axiom 4 (c10): mult(i(X), X) = unit.
% 0.19/0.55 Axiom 5 (c02): ld(X, mult(X, Y)) = Y.
% 0.19/0.55 Axiom 6 (c04): rd(mult(X, Y), Y) = X.
% 0.19/0.55 Axiom 7 (c07): mult(X, i(mult(Y, X))) = i(Y).
% 0.19/0.55 Axiom 8 (c09): mult(mult(X, Y), Z) = mult(mult(X, Z), ld(Z, mult(Y, Z))).
% 0.19/0.55 Axiom 9 (c08): mult(X, mult(Y, Z)) = mult(rd(mult(X, Y), X), mult(X, Z)).
% 0.19/0.55
% 0.19/0.55 Lemma 10: i(i(X)) = X.
% 0.19/0.55 Proof:
% 0.19/0.55 i(i(X))
% 0.19/0.55 = { by axiom 5 (c02) R->L }
% 0.19/0.55 ld(i(X), mult(i(X), i(i(X))))
% 0.19/0.55 = { by axiom 3 (c11) }
% 0.19/0.55 ld(i(X), unit)
% 0.19/0.55 = { by axiom 4 (c10) R->L }
% 0.19/0.55 ld(i(X), mult(i(X), X))
% 0.19/0.55 = { by axiom 5 (c02) }
% 0.19/0.55 X
% 0.19/0.55
% 0.19/0.55 Goal 1 (goals): mult(mult(a, b), mult(b, mult(c, b))) = mult(mult(a, mult(b, mult(b, c))), b).
% 0.19/0.55 Proof:
% 0.19/0.55 mult(mult(a, b), mult(b, mult(c, b)))
% 0.19/0.55 = { by axiom 5 (c02) R->L }
% 0.19/0.55 mult(mult(a, b), ld(i(mult(b, c)), mult(i(mult(b, c)), mult(b, mult(c, b)))))
% 0.19/0.55 = { by axiom 6 (c04) R->L }
% 0.19/0.55 mult(mult(a, b), ld(i(mult(b, c)), mult(rd(mult(i(mult(b, c)), i(mult(c, i(mult(b, c))))), i(mult(c, i(mult(b, c))))), mult(b, mult(c, b)))))
% 0.19/0.55 = { by axiom 7 (c07) }
% 0.19/0.55 mult(mult(a, b), ld(i(mult(b, c)), mult(rd(i(c), i(mult(c, i(mult(b, c))))), mult(b, mult(c, b)))))
% 0.19/0.55 = { by axiom 7 (c07) }
% 0.19/0.55 mult(mult(a, b), ld(i(mult(b, c)), mult(rd(i(c), i(i(b))), mult(b, mult(c, b)))))
% 0.19/0.55 = { by lemma 10 }
% 0.19/0.56 mult(mult(a, b), ld(i(mult(b, c)), mult(rd(i(c), b), mult(b, mult(c, b)))))
% 0.19/0.56 = { by axiom 7 (c07) R->L }
% 0.19/0.56 mult(mult(a, b), ld(i(mult(b, c)), mult(rd(mult(b, i(mult(c, b))), b), mult(b, mult(c, b)))))
% 0.19/0.56 = { by axiom 9 (c08) R->L }
% 0.19/0.56 mult(mult(a, b), ld(i(mult(b, c)), mult(b, mult(i(mult(c, b)), mult(c, b)))))
% 0.19/0.56 = { by axiom 4 (c10) }
% 0.19/0.56 mult(mult(a, b), ld(i(mult(b, c)), mult(b, unit)))
% 0.19/0.56 = { by axiom 1 (c05) }
% 0.19/0.56 mult(mult(a, b), ld(i(mult(b, c)), b))
% 0.19/0.56 = { by axiom 7 (c07) R->L }
% 0.19/0.56 mult(mult(a, b), ld(mult(i(mult(b, mult(b, c))), i(mult(mult(b, c), i(mult(b, mult(b, c)))))), b))
% 0.19/0.56 = { by axiom 7 (c07) }
% 0.19/0.56 mult(mult(a, b), ld(mult(i(mult(b, mult(b, c))), i(i(b))), b))
% 0.19/0.56 = { by lemma 10 }
% 0.19/0.56 mult(mult(a, b), ld(mult(i(mult(b, mult(b, c))), b), b))
% 0.19/0.56 = { by axiom 2 (c06) R->L }
% 0.19/0.56 mult(mult(a, b), ld(mult(i(mult(b, mult(b, c))), b), mult(unit, b)))
% 0.19/0.56 = { by axiom 4 (c10) R->L }
% 0.19/0.56 mult(mult(a, b), ld(mult(i(mult(b, mult(b, c))), b), mult(mult(i(mult(b, mult(b, c))), mult(b, mult(b, c))), b)))
% 0.19/0.56 = { by axiom 8 (c09) }
% 0.19/0.56 mult(mult(a, b), ld(mult(i(mult(b, mult(b, c))), b), mult(mult(i(mult(b, mult(b, c))), b), ld(b, mult(mult(b, mult(b, c)), b)))))
% 0.19/0.56 = { by axiom 5 (c02) }
% 0.19/0.56 mult(mult(a, b), ld(b, mult(mult(b, mult(b, c)), b)))
% 0.19/0.56 = { by axiom 8 (c09) R->L }
% 0.19/0.56 mult(mult(a, mult(b, mult(b, c))), b)
% 0.19/0.56 % SZS output end Proof
% 0.19/0.56
% 0.19/0.56 RESULT: Unsatisfiable (the axioms are contradictory).
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