TSTP Solution File: GRP573-1 by Twee---2.4.2
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP573-1 : 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 : n025.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 01:18:58 EDT 2023
% Result : Unsatisfiable 0.19s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP573-1 : TPTP v8.1.2. Released v2.6.0.
% 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 : n025.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 23:41:54 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.38 Command-line arguments: --kbo-weight0 --lhs-weight 5 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10 --goal-heuristic
% 0.19/0.38
% 0.19/0.38 % SZS status Unsatisfiable
% 0.19/0.38
% 0.19/0.39 % SZS output start Proof
% 0.19/0.39 Axiom 1 (inverse): inverse(X) = double_divide(X, identity).
% 0.19/0.39 Axiom 2 (identity): identity = double_divide(X, inverse(X)).
% 0.19/0.39 Axiom 3 (multiply): multiply(X, Y) = double_divide(double_divide(Y, X), identity).
% 0.19/0.39 Axiom 4 (single_axiom): double_divide(double_divide(X, double_divide(double_divide(Y, double_divide(Z, X)), double_divide(Z, identity))), double_divide(identity, identity)) = Y.
% 0.19/0.39
% 0.19/0.39 Lemma 5: double_divide(X, double_divide(X, identity)) = identity.
% 0.19/0.39 Proof:
% 0.19/0.39 double_divide(X, double_divide(X, identity))
% 0.19/0.39 = { by axiom 1 (inverse) R->L }
% 0.19/0.39 double_divide(X, inverse(X))
% 0.19/0.39 = { by axiom 2 (identity) R->L }
% 0.19/0.39 identity
% 0.19/0.39
% 0.19/0.39 Lemma 6: multiply(inverse(X), X) = double_divide(identity, identity).
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(inverse(X), X)
% 0.19/0.39 = { by axiom 3 (multiply) }
% 0.19/0.39 double_divide(double_divide(X, inverse(X)), identity)
% 0.19/0.39 = { by axiom 1 (inverse) }
% 0.19/0.39 double_divide(double_divide(X, double_divide(X, identity)), identity)
% 0.19/0.39 = { by lemma 5 }
% 0.19/0.39 double_divide(identity, identity)
% 0.19/0.39
% 0.19/0.39 Lemma 7: double_divide(identity, multiply(inverse(X), X)) = identity.
% 0.19/0.39 Proof:
% 0.19/0.39 double_divide(identity, multiply(inverse(X), X))
% 0.19/0.39 = { by lemma 6 }
% 0.19/0.39 double_divide(identity, double_divide(identity, identity))
% 0.19/0.39 = { by lemma 5 }
% 0.19/0.39 identity
% 0.19/0.39
% 0.19/0.39 Lemma 8: double_divide(double_divide(identity, double_divide(double_divide(X, multiply(inverse(Y), Y)), multiply(inverse(Z), Z))), multiply(inverse(W), W)) = X.
% 0.19/0.39 Proof:
% 0.19/0.39 double_divide(double_divide(identity, double_divide(double_divide(X, multiply(inverse(Y), Y)), multiply(inverse(Z), Z))), multiply(inverse(W), W))
% 0.19/0.39 = { by lemma 6 }
% 0.19/0.39 double_divide(double_divide(identity, double_divide(double_divide(X, multiply(inverse(Y), Y)), double_divide(identity, identity))), multiply(inverse(W), W))
% 0.19/0.39 = { by lemma 6 }
% 0.19/0.39 double_divide(double_divide(identity, double_divide(double_divide(X, multiply(inverse(Y), Y)), double_divide(identity, identity))), double_divide(identity, identity))
% 0.19/0.39 = { by lemma 6 }
% 0.19/0.39 double_divide(double_divide(identity, double_divide(double_divide(X, double_divide(identity, identity)), double_divide(identity, identity))), double_divide(identity, identity))
% 0.19/0.39 = { by axiom 4 (single_axiom) }
% 0.19/0.39 X
% 0.19/0.39
% 0.19/0.39 Lemma 9: double_divide(multiply(inverse(X), X), multiply(inverse(Y), Y)) = identity.
% 0.19/0.39 Proof:
% 0.19/0.39 double_divide(multiply(inverse(X), X), multiply(inverse(Y), Y))
% 0.19/0.39 = { by lemma 6 }
% 0.19/0.39 double_divide(double_divide(identity, identity), multiply(inverse(Y), Y))
% 0.19/0.39 = { by lemma 7 R->L }
% 0.19/0.39 double_divide(double_divide(identity, double_divide(identity, multiply(inverse(Z), Z))), multiply(inverse(Y), Y))
% 0.19/0.39 = { by lemma 7 R->L }
% 0.19/0.39 double_divide(double_divide(identity, double_divide(double_divide(identity, multiply(inverse(W), W)), multiply(inverse(Z), Z))), multiply(inverse(Y), Y))
% 0.19/0.39 = { by lemma 8 }
% 0.19/0.39 identity
% 0.19/0.39
% 0.19/0.39 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = identity.
% 0.19/0.39 Proof:
% 0.19/0.39 multiply(inverse(a1), a1)
% 0.19/0.39 = { by lemma 8 R->L }
% 0.19/0.39 double_divide(double_divide(identity, double_divide(double_divide(multiply(inverse(a1), a1), multiply(inverse(X), X)), multiply(inverse(Y), Y))), multiply(inverse(Z), Z))
% 0.19/0.39 = { by lemma 9 }
% 0.19/0.39 double_divide(double_divide(identity, double_divide(identity, multiply(inverse(Y), Y))), multiply(inverse(Z), Z))
% 0.19/0.39 = { by lemma 7 }
% 0.19/0.39 double_divide(double_divide(identity, identity), multiply(inverse(Z), Z))
% 0.19/0.39 = { by lemma 6 R->L }
% 0.19/0.39 double_divide(multiply(inverse(W), W), multiply(inverse(Z), Z))
% 0.19/0.39 = { by lemma 9 }
% 0.19/0.39 identity
% 0.19/0.39 % SZS output end Proof
% 0.19/0.39
% 0.19/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
%------------------------------------------------------------------------------