TSTP Solution File: GRP488-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP488-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n024.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 01:18:38 EDT 2023
% Result : Unsatisfiable 0.13s 0.40s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRP488-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n024.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 20:32:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.40 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.13/0.40
% 0.13/0.40 % SZS status Unsatisfiable
% 0.13/0.40
% 0.19/0.42 % SZS output start Proof
% 0.19/0.42 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.19/0.42 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.19/0.42 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.19/0.42 Axiom 4 (single_axiom): double_divide(X, double_divide(double_divide(double_divide(identity, double_divide(double_divide(X, identity), double_divide(Y, Z))), Y), identity)) = Z.
% 0.19/0.42
% 0.19/0.42 Lemma 5: double_divide(X, double_divide(X, identity)) = identity.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(X, double_divide(X, identity))
% 0.19/0.42 = { by axiom 1 (inverse) R->L }
% 0.19/0.42 double_divide(X, inverse(X))
% 0.19/0.42 = { by axiom 2 (identity) R->L }
% 0.19/0.42 identity
% 0.19/0.42
% 0.19/0.42 Lemma 6: double_divide(X, multiply(Y, double_divide(identity, double_divide(double_divide(X, identity), double_divide(Y, Z))))) = Z.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(X, multiply(Y, double_divide(identity, double_divide(double_divide(X, identity), double_divide(Y, Z)))))
% 0.19/0.42 = { by axiom 3 (multiply) }
% 0.19/0.42 double_divide(X, double_divide(double_divide(double_divide(identity, double_divide(double_divide(X, identity), double_divide(Y, Z))), Y), identity))
% 0.19/0.42 = { by axiom 4 (single_axiom) }
% 0.19/0.42 Z
% 0.19/0.42
% 0.19/0.42 Lemma 7: double_divide(X, multiply(Y, double_divide(identity, multiply(identity, X)))) = double_divide(Y, identity).
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(X, multiply(Y, double_divide(identity, multiply(identity, X))))
% 0.19/0.42 = { by axiom 3 (multiply) }
% 0.19/0.42 double_divide(X, multiply(Y, double_divide(identity, double_divide(double_divide(X, identity), identity))))
% 0.19/0.42 = { by lemma 5 R->L }
% 0.19/0.42 double_divide(X, multiply(Y, double_divide(identity, double_divide(double_divide(X, identity), double_divide(Y, double_divide(Y, identity))))))
% 0.19/0.42 = { by lemma 6 }
% 0.19/0.42 double_divide(Y, identity)
% 0.19/0.42
% 0.19/0.42 Lemma 8: double_divide(X, multiply(double_divide(X, identity), double_divide(identity, identity))) = identity.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(X, multiply(double_divide(X, identity), double_divide(identity, identity)))
% 0.19/0.42 = { by lemma 5 R->L }
% 0.19/0.42 double_divide(X, multiply(double_divide(X, identity), double_divide(identity, double_divide(double_divide(X, identity), double_divide(double_divide(X, identity), identity)))))
% 0.19/0.42 = { by lemma 6 }
% 0.19/0.42 identity
% 0.19/0.42
% 0.19/0.42 Lemma 9: multiply(double_divide(X, identity), X) = double_divide(identity, identity).
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(double_divide(X, identity), X)
% 0.19/0.42 = { by axiom 3 (multiply) }
% 0.19/0.42 double_divide(double_divide(X, double_divide(X, identity)), identity)
% 0.19/0.42 = { by lemma 5 }
% 0.19/0.42 double_divide(identity, identity)
% 0.19/0.42
% 0.19/0.42 Lemma 10: multiply(identity, identity) = double_divide(identity, identity).
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(identity, identity)
% 0.19/0.42 = { by axiom 3 (multiply) }
% 0.19/0.42 double_divide(double_divide(identity, identity), identity)
% 0.19/0.42 = { by lemma 7 R->L }
% 0.19/0.42 double_divide(X, multiply(double_divide(identity, identity), double_divide(identity, multiply(identity, X))))
% 0.19/0.42 = { by axiom 3 (multiply) }
% 0.19/0.42 double_divide(X, multiply(double_divide(identity, identity), double_divide(identity, double_divide(double_divide(X, identity), identity))))
% 0.19/0.42 = { by lemma 8 R->L }
% 0.19/0.42 double_divide(X, multiply(double_divide(identity, identity), double_divide(identity, double_divide(double_divide(X, identity), double_divide(double_divide(identity, identity), multiply(double_divide(double_divide(identity, identity), identity), double_divide(identity, identity)))))))
% 0.19/0.42 = { by lemma 9 }
% 0.19/0.42 double_divide(X, multiply(double_divide(identity, identity), double_divide(identity, double_divide(double_divide(X, identity), double_divide(double_divide(identity, identity), double_divide(identity, identity))))))
% 0.19/0.42 = { by lemma 6 }
% 0.19/0.42 double_divide(identity, identity)
% 0.19/0.42
% 0.19/0.42 Lemma 11: double_divide(identity, multiply(X, identity)) = double_divide(X, identity).
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(identity, multiply(X, identity))
% 0.19/0.42 = { by lemma 5 R->L }
% 0.19/0.42 double_divide(identity, multiply(X, double_divide(identity, double_divide(identity, identity))))
% 0.19/0.42 = { by lemma 10 R->L }
% 0.19/0.42 double_divide(identity, multiply(X, double_divide(identity, multiply(identity, identity))))
% 0.19/0.42 = { by lemma 7 }
% 0.19/0.42 double_divide(X, identity)
% 0.19/0.42
% 0.19/0.42 Lemma 12: double_divide(identity, identity) = identity.
% 0.19/0.42 Proof:
% 0.19/0.42 double_divide(identity, identity)
% 0.19/0.42 = { by lemma 10 R->L }
% 0.19/0.42 multiply(identity, identity)
% 0.19/0.42 = { by axiom 3 (multiply) }
% 0.19/0.42 double_divide(double_divide(identity, identity), identity)
% 0.19/0.42 = { by lemma 11 R->L }
% 0.19/0.42 double_divide(identity, multiply(double_divide(identity, identity), identity))
% 0.19/0.42 = { by lemma 9 }
% 0.19/0.42 double_divide(identity, double_divide(identity, identity))
% 0.19/0.42 = { by lemma 5 }
% 0.19/0.42 identity
% 0.19/0.42
% 0.19/0.42 Lemma 13: multiply(multiply(X, identity), identity) = multiply(identity, X).
% 0.19/0.42 Proof:
% 0.19/0.42 multiply(multiply(X, identity), identity)
% 0.19/0.43 = { by axiom 3 (multiply) }
% 0.19/0.43 double_divide(double_divide(identity, multiply(X, identity)), identity)
% 0.19/0.43 = { by lemma 11 }
% 0.19/0.43 double_divide(double_divide(X, identity), identity)
% 0.19/0.43 = { by axiom 3 (multiply) R->L }
% 0.19/0.43 multiply(identity, X)
% 0.19/0.43
% 0.19/0.43 Lemma 14: multiply(double_divide(X, identity), identity) = double_divide(X, identity).
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(double_divide(X, identity), identity)
% 0.19/0.43 = { by lemma 6 R->L }
% 0.19/0.43 double_divide(Y, multiply(X, double_divide(identity, double_divide(double_divide(Y, identity), double_divide(X, multiply(double_divide(X, identity), identity))))))
% 0.19/0.43 = { by lemma 12 R->L }
% 0.19/0.43 double_divide(Y, multiply(X, double_divide(identity, double_divide(double_divide(Y, identity), double_divide(X, multiply(double_divide(X, identity), double_divide(identity, identity)))))))
% 0.19/0.43 = { by lemma 8 }
% 0.19/0.43 double_divide(Y, multiply(X, double_divide(identity, double_divide(double_divide(Y, identity), identity))))
% 0.19/0.43 = { by axiom 3 (multiply) R->L }
% 0.19/0.43 double_divide(Y, multiply(X, double_divide(identity, multiply(identity, Y))))
% 0.19/0.43 = { by lemma 7 }
% 0.19/0.43 double_divide(X, identity)
% 0.19/0.43
% 0.19/0.43 Lemma 15: multiply(multiply(X, Y), identity) = multiply(X, Y).
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(multiply(X, Y), identity)
% 0.19/0.43 = { by axiom 3 (multiply) }
% 0.19/0.43 multiply(double_divide(double_divide(Y, X), identity), identity)
% 0.19/0.43 = { by lemma 14 }
% 0.19/0.43 double_divide(double_divide(Y, X), identity)
% 0.19/0.43 = { by axiom 3 (multiply) R->L }
% 0.19/0.43 multiply(X, Y)
% 0.19/0.43
% 0.19/0.43 Lemma 16: multiply(identity, X) = multiply(X, identity).
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(identity, X)
% 0.19/0.43 = { by lemma 13 R->L }
% 0.19/0.43 multiply(multiply(X, identity), identity)
% 0.19/0.43 = { by lemma 15 }
% 0.19/0.43 multiply(X, identity)
% 0.19/0.43
% 0.19/0.43 Lemma 17: double_divide(identity, double_divide(X, identity)) = multiply(X, identity).
% 0.19/0.43 Proof:
% 0.19/0.43 double_divide(identity, double_divide(X, identity))
% 0.19/0.43 = { by lemma 14 R->L }
% 0.19/0.43 double_divide(identity, multiply(double_divide(X, identity), identity))
% 0.19/0.43 = { by lemma 11 }
% 0.19/0.43 double_divide(double_divide(X, identity), identity)
% 0.19/0.43 = { by axiom 3 (multiply) R->L }
% 0.19/0.43 multiply(identity, X)
% 0.19/0.43 = { by lemma 16 }
% 0.19/0.43 multiply(X, identity)
% 0.19/0.43
% 0.19/0.43 Lemma 18: multiply(identity, double_divide(X, Y)) = double_divide(multiply(Y, X), identity).
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(identity, double_divide(X, Y))
% 0.19/0.43 = { by axiom 3 (multiply) }
% 0.19/0.43 double_divide(double_divide(double_divide(X, Y), identity), identity)
% 0.19/0.43 = { by axiom 3 (multiply) R->L }
% 0.19/0.43 double_divide(multiply(Y, X), identity)
% 0.19/0.43
% 0.19/0.43 Lemma 19: double_divide(multiply(multiply(identity, X), identity), identity) = double_divide(X, double_divide(identity, identity)).
% 0.19/0.43 Proof:
% 0.19/0.43 double_divide(multiply(multiply(identity, X), identity), identity)
% 0.19/0.43 = { by lemma 18 R->L }
% 0.19/0.43 multiply(identity, double_divide(identity, multiply(identity, X)))
% 0.19/0.43 = { by axiom 3 (multiply) }
% 0.19/0.43 double_divide(double_divide(double_divide(identity, multiply(identity, X)), identity), identity)
% 0.19/0.43 = { by lemma 7 R->L }
% 0.19/0.43 double_divide(X, multiply(double_divide(double_divide(identity, multiply(identity, X)), identity), double_divide(identity, multiply(identity, X))))
% 0.19/0.43 = { by lemma 9 }
% 0.19/0.43 double_divide(X, double_divide(identity, identity))
% 0.19/0.43
% 0.19/0.43 Goal 1 (prove_these_axioms_2): multiply(identity, a2) = a2.
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(identity, a2)
% 0.19/0.43 = { by lemma 12 R->L }
% 0.19/0.43 multiply(double_divide(identity, identity), a2)
% 0.19/0.43 = { by axiom 3 (multiply) }
% 0.19/0.43 double_divide(double_divide(a2, double_divide(identity, identity)), identity)
% 0.19/0.43 = { by lemma 19 R->L }
% 0.19/0.43 double_divide(double_divide(multiply(multiply(identity, a2), identity), identity), identity)
% 0.19/0.43 = { by axiom 3 (multiply) R->L }
% 0.19/0.43 multiply(identity, multiply(multiply(identity, a2), identity))
% 0.19/0.43 = { by lemma 15 }
% 0.19/0.43 multiply(identity, multiply(identity, a2))
% 0.19/0.43 = { by lemma 13 R->L }
% 0.19/0.43 multiply(multiply(multiply(identity, a2), identity), identity)
% 0.19/0.43 = { by lemma 17 R->L }
% 0.19/0.43 double_divide(identity, double_divide(multiply(multiply(identity, a2), identity), identity))
% 0.19/0.43 = { by lemma 19 }
% 0.19/0.43 double_divide(identity, double_divide(a2, double_divide(identity, identity)))
% 0.19/0.43 = { by lemma 12 }
% 0.19/0.43 double_divide(identity, double_divide(a2, identity))
% 0.19/0.43 = { by lemma 17 }
% 0.19/0.43 multiply(a2, identity)
% 0.19/0.43 = { by axiom 3 (multiply) }
% 0.19/0.43 double_divide(double_divide(identity, a2), identity)
% 0.19/0.43 = { by lemma 14 R->L }
% 0.19/0.43 multiply(double_divide(double_divide(identity, a2), identity), identity)
% 0.19/0.43 = { by lemma 14 R->L }
% 0.19/0.43 multiply(multiply(double_divide(double_divide(identity, a2), identity), identity), identity)
% 0.19/0.43 = { by lemma 13 }
% 0.19/0.43 multiply(identity, double_divide(double_divide(identity, a2), identity))
% 0.19/0.43 = { by lemma 18 }
% 0.19/0.43 double_divide(multiply(identity, double_divide(identity, a2)), identity)
% 0.19/0.43 = { by lemma 16 }
% 0.19/0.43 double_divide(multiply(double_divide(identity, a2), identity), identity)
% 0.19/0.43 = { by lemma 12 R->L }
% 0.19/0.43 double_divide(multiply(double_divide(identity, a2), double_divide(identity, identity)), identity)
% 0.19/0.43 = { by lemma 18 R->L }
% 0.19/0.43 multiply(identity, double_divide(double_divide(identity, identity), double_divide(identity, a2)))
% 0.19/0.43 = { by lemma 13 R->L }
% 0.19/0.43 multiply(multiply(double_divide(double_divide(identity, identity), double_divide(identity, a2)), identity), identity)
% 0.19/0.43 = { by lemma 17 R->L }
% 0.19/0.43 double_divide(identity, double_divide(multiply(double_divide(double_divide(identity, identity), double_divide(identity, a2)), identity), identity))
% 0.19/0.43 = { by lemma 18 R->L }
% 0.19/0.43 double_divide(identity, multiply(identity, double_divide(identity, double_divide(double_divide(identity, identity), double_divide(identity, a2)))))
% 0.19/0.43 = { by lemma 6 }
% 0.19/0.43 a2
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43
% 0.19/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------