TSTP Solution File: GRP718-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP718-1 : 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 : n029.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 01:19:52 EDT 2023
% Result : Unsatisfiable 5.27s 1.06s
% Output : Proof 5.72s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP718-1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n029.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 02:27:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 5.27/1.06 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 5.27/1.06
% 5.27/1.06 % SZS status Unsatisfiable
% 5.27/1.06
% 5.27/1.08 % SZS output start Proof
% 5.27/1.08 Axiom 1 (c10): mult(X, Y) = mult(Y, X).
% 5.27/1.08 Axiom 2 (c05): mult(X, unit) = X.
% 5.27/1.08 Axiom 3 (c06): mult(unit, X) = X.
% 5.27/1.08 Axiom 4 (c02): ld(X, mult(X, Y)) = Y.
% 5.27/1.08 Axiom 5 (c08): mult(mult(X, Y), i(Y)) = X.
% 5.27/1.08 Axiom 6 (c07): mult(i(X), mult(X, Y)) = Y.
% 5.27/1.08 Axiom 7 (c09): mult(mult(X, Y), mult(Z, mult(X, Y))) = mult(mult(mult(X, mult(Y, Z)), X), Y).
% 5.27/1.08
% 5.27/1.08 Lemma 8: mult(mult(X, Y), mult(Z, mult(X, Y))) = mult(Y, mult(X, mult(X, mult(Y, Z)))).
% 5.27/1.08 Proof:
% 5.27/1.08 mult(mult(X, Y), mult(Z, mult(X, Y)))
% 5.27/1.08 = { by axiom 7 (c09) }
% 5.27/1.08 mult(mult(mult(X, mult(Y, Z)), X), Y)
% 5.27/1.08 = { by axiom 1 (c10) }
% 5.27/1.08 mult(Y, mult(mult(X, mult(Y, Z)), X))
% 5.27/1.08 = { by axiom 1 (c10) }
% 5.27/1.08 mult(Y, mult(X, mult(X, mult(Y, Z))))
% 5.27/1.08
% 5.27/1.08 Lemma 9: mult(mult(X, Y), mult(mult(X, Y), Z)) = mult(Y, mult(X, mult(X, mult(Y, Z)))).
% 5.27/1.08 Proof:
% 5.27/1.08 mult(mult(X, Y), mult(mult(X, Y), Z))
% 5.27/1.08 = { by axiom 1 (c10) R->L }
% 5.27/1.08 mult(mult(X, Y), mult(Z, mult(X, Y)))
% 5.27/1.08 = { by lemma 8 }
% 5.27/1.08 mult(Y, mult(X, mult(X, mult(Y, Z))))
% 5.27/1.08
% 5.27/1.08 Lemma 10: mult(Y, mult(Y, X)) = mult(X, mult(Y, Y)).
% 5.27/1.08 Proof:
% 5.27/1.08 mult(Y, mult(Y, X))
% 5.27/1.08 = { by axiom 1 (c10) R->L }
% 5.27/1.08 mult(mult(Y, X), Y)
% 5.27/1.08 = { by axiom 5 (c08) R->L }
% 5.27/1.08 mult(mult(Y, X), mult(mult(Y, X), i(X)))
% 5.27/1.08 = { by lemma 9 }
% 5.27/1.08 mult(X, mult(Y, mult(Y, mult(X, i(X)))))
% 5.27/1.08 = { by axiom 3 (c06) R->L }
% 5.27/1.08 mult(X, mult(Y, mult(Y, mult(mult(unit, X), i(X)))))
% 5.27/1.08 = { by axiom 5 (c08) }
% 5.27/1.08 mult(X, mult(Y, mult(Y, unit)))
% 5.27/1.08 = { by axiom 2 (c05) }
% 5.27/1.08 mult(X, mult(Y, Y))
% 5.27/1.08
% 5.27/1.08 Lemma 11: mult(mult(X, Y), mult(X, Y)) = mult(X, mult(Y, mult(X, Y))).
% 5.27/1.08 Proof:
% 5.27/1.08 mult(mult(X, Y), mult(X, Y))
% 5.27/1.08 = { by axiom 1 (c10) R->L }
% 5.27/1.08 mult(mult(Y, X), mult(X, Y))
% 5.27/1.08 = { by axiom 1 (c10) R->L }
% 5.27/1.08 mult(mult(Y, X), mult(Y, X))
% 5.72/1.08 = { by axiom 3 (c06) R->L }
% 5.72/1.08 mult(mult(Y, X), mult(unit, mult(Y, X)))
% 5.72/1.08 = { by lemma 8 }
% 5.72/1.08 mult(X, mult(Y, mult(Y, mult(X, unit))))
% 5.72/1.08 = { by axiom 2 (c05) }
% 5.72/1.08 mult(X, mult(Y, mult(Y, X)))
% 5.72/1.08 = { by axiom 1 (c10) }
% 5.72/1.08 mult(X, mult(Y, mult(X, Y)))
% 5.72/1.08
% 5.72/1.08 Lemma 12: mult(mult(X, Y), mult(Y, X)) = mult(Y, mult(X, mult(X, Y))).
% 5.72/1.08 Proof:
% 5.72/1.08 mult(mult(X, Y), mult(Y, X))
% 5.72/1.08 = { by axiom 1 (c10) R->L }
% 5.72/1.08 mult(mult(Y, X), mult(Y, X))
% 5.72/1.08 = { by lemma 11 }
% 5.72/1.08 mult(Y, mult(X, mult(Y, X)))
% 5.72/1.08 = { by axiom 1 (c10) }
% 5.72/1.08 mult(Y, mult(X, mult(X, Y)))
% 5.72/1.08
% 5.72/1.08 Lemma 13: mult(Z, mult(X, mult(X, mult(Y, Y)))) = mult(X, mult(mult(Y, Y), mult(X, Z))).
% 5.72/1.08 Proof:
% 5.72/1.08 mult(Z, mult(X, mult(X, mult(Y, Y))))
% 5.72/1.08 = { by lemma 10 R->L }
% 5.72/1.08 mult(Z, mult(X, mult(Y, mult(Y, X))))
% 5.72/1.08 = { by lemma 12 R->L }
% 5.72/1.08 mult(Z, mult(mult(Y, X), mult(X, Y)))
% 5.72/1.08 = { by axiom 1 (c10) }
% 5.72/1.08 mult(Z, mult(mult(X, Y), mult(Y, X)))
% 5.72/1.08 = { by lemma 12 }
% 5.72/1.08 mult(Z, mult(Y, mult(X, mult(X, Y))))
% 5.72/1.08 = { by axiom 1 (c10) }
% 5.72/1.08 mult(Z, mult(Y, mult(X, mult(Y, X))))
% 5.72/1.08 = { by lemma 11 R->L }
% 5.72/1.08 mult(Z, mult(mult(Y, X), mult(Y, X)))
% 5.72/1.08 = { by lemma 10 R->L }
% 5.72/1.08 mult(mult(Y, X), mult(mult(Y, X), Z))
% 5.72/1.08 = { by lemma 9 }
% 5.72/1.08 mult(X, mult(Y, mult(Y, mult(X, Z))))
% 5.72/1.08 = { by lemma 10 }
% 5.72/1.08 mult(X, mult(mult(X, Z), mult(Y, Y)))
% 5.72/1.08 = { by axiom 1 (c10) }
% 5.72/1.08 mult(X, mult(mult(Y, Y), mult(X, Z)))
% 5.72/1.08
% 5.72/1.08 Lemma 14: mult(mult(X, Y), mult(X, mult(Z, Z))) = mult(X, mult(X, mult(Y, mult(Z, Z)))).
% 5.72/1.08 Proof:
% 5.72/1.08 mult(mult(X, Y), mult(X, mult(Z, Z)))
% 5.72/1.08 = { by axiom 1 (c10) R->L }
% 5.72/1.08 mult(mult(X, Y), mult(mult(Z, Z), X))
% 5.72/1.08 = { by axiom 5 (c08) R->L }
% 5.72/1.08 mult(mult(X, Y), mult(mult(Z, Z), mult(mult(X, Y), i(Y))))
% 5.72/1.08 = { by lemma 13 R->L }
% 5.72/1.08 mult(i(Y), mult(mult(X, Y), mult(mult(X, Y), mult(Z, Z))))
% 5.72/1.08 = { by lemma 9 }
% 5.72/1.08 mult(i(Y), mult(Y, mult(X, mult(X, mult(Y, mult(Z, Z))))))
% 5.72/1.08 = { by axiom 6 (c07) }
% 5.72/1.08 mult(X, mult(X, mult(Y, mult(Z, Z))))
% 5.72/1.08
% 5.72/1.08 Goal 1 (goals): mult(mult(a, a), mult(mult(b, c), mult(a, a))) = mult(mult(mult(a, a), b), mult(c, mult(a, a))).
% 5.72/1.08 Proof:
% 5.72/1.08 mult(mult(a, a), mult(mult(b, c), mult(a, a)))
% 5.72/1.08 = { by axiom 4 (c02) R->L }
% 5.72/1.08 ld(b, mult(b, mult(mult(a, a), mult(mult(b, c), mult(a, a)))))
% 5.72/1.08 = { by axiom 4 (c02) R->L }
% 5.72/1.08 ld(b, ld(b, mult(b, mult(b, mult(mult(a, a), mult(mult(b, c), mult(a, a)))))))
% 5.72/1.08 = { by axiom 4 (c02) R->L }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(mult(a, a), b), mult(b, mult(b, mult(mult(a, a), mult(mult(b, c), mult(a, a)))))))))
% 5.72/1.08 = { by axiom 1 (c10) R->L }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(mult(a, a), b), mult(b, mult(b, mult(mult(mult(b, c), mult(a, a)), mult(a, a))))))))
% 5.72/1.08 = { by lemma 14 R->L }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(mult(a, a), b), mult(mult(b, mult(mult(b, c), mult(a, a))), mult(b, mult(a, a)))))))
% 5.72/1.08 = { by axiom 1 (c10) R->L }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(mult(a, a), b), mult(mult(b, mult(mult(b, c), mult(a, a))), mult(mult(a, a), b))))))
% 5.72/1.08 = { by axiom 1 (c10) R->L }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(mult(a, a), b), mult(mult(mult(a, a), b), mult(b, mult(mult(b, c), mult(a, a))))))))
% 5.72/1.08 = { by lemma 10 }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(b, mult(mult(b, c), mult(a, a))), mult(mult(mult(a, a), b), mult(mult(a, a), b))))))
% 5.72/1.08 = { by lemma 11 }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(b, mult(mult(b, c), mult(a, a))), mult(mult(a, a), mult(b, mult(mult(a, a), b)))))))
% 5.72/1.08 = { by axiom 1 (c10) }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(b, mult(mult(a, a), mult(b, c))), mult(mult(a, a), mult(b, mult(mult(a, a), b)))))))
% 5.72/1.08 = { by lemma 13 R->L }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(c, mult(b, mult(b, mult(a, a)))), mult(mult(a, a), mult(b, mult(mult(a, a), b)))))))
% 5.72/1.08 = { by axiom 1 (c10) R->L }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(c, mult(b, mult(mult(a, a), b))), mult(mult(a, a), mult(b, mult(mult(a, a), b)))))))
% 5.72/1.08 = { by axiom 1 (c10) R->L }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(c, mult(b, mult(mult(a, a), b))), mult(mult(b, mult(mult(a, a), b)), mult(a, a))))))
% 5.72/1.08 = { by axiom 1 (c10) R->L }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(mult(b, mult(mult(a, a), b)), c), mult(mult(b, mult(mult(a, a), b)), mult(a, a))))))
% 5.72/1.08 = { by lemma 14 }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(b, mult(mult(a, a), b)), mult(mult(b, mult(mult(a, a), b)), mult(c, mult(a, a)))))))
% 5.72/1.08 = { by lemma 9 }
% 5.72/1.08 ld(b, ld(b, ld(mult(mult(a, a), b), mult(mult(mult(a, a), b), mult(b, mult(b, mult(mult(mult(a, a), b), mult(c, mult(a, a)))))))))
% 5.72/1.08 = { by axiom 4 (c02) }
% 5.72/1.08 ld(b, ld(b, mult(b, mult(b, mult(mult(mult(a, a), b), mult(c, mult(a, a)))))))
% 5.72/1.08 = { by axiom 4 (c02) }
% 5.72/1.08 ld(b, mult(b, mult(mult(mult(a, a), b), mult(c, mult(a, a)))))
% 5.72/1.08 = { by axiom 4 (c02) }
% 5.72/1.08 mult(mult(mult(a, a), b), mult(c, mult(a, a)))
% 5.72/1.08 % SZS output end Proof
% 5.72/1.08
% 5.72/1.08 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------