TSTP Solution File: GRP586-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP586-1 : 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 : n006.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 01:19:01 EDT 2023
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP586-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n006.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 23:28:21 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.40 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.40
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 Axiom 1 (multiply): multiply(X, Y) = inverse(double_divide(Y, X)).
% 0.21/0.40 Axiom 2 (single_axiom): double_divide(X, inverse(double_divide(inverse(double_divide(double_divide(X, Y), inverse(Z))), Y))) = Z.
% 0.21/0.40
% 0.21/0.40 Lemma 3: double_divide(X, multiply(Y, multiply(inverse(Z), double_divide(X, Y)))) = Z.
% 0.21/0.40 Proof:
% 0.21/0.40 double_divide(X, multiply(Y, multiply(inverse(Z), double_divide(X, Y))))
% 0.21/0.40 = { by axiom 1 (multiply) }
% 0.21/0.40 double_divide(X, multiply(Y, inverse(double_divide(double_divide(X, Y), inverse(Z)))))
% 0.21/0.40 = { by axiom 1 (multiply) }
% 0.21/0.40 double_divide(X, inverse(double_divide(inverse(double_divide(double_divide(X, Y), inverse(Z))), Y)))
% 0.21/0.41 = { by axiom 2 (single_axiom) }
% 0.21/0.41 Z
% 0.21/0.41
% 0.21/0.41 Lemma 4: double_divide(multiply(inverse(X), Y), inverse(Y)) = X.
% 0.21/0.41 Proof:
% 0.21/0.41 double_divide(multiply(inverse(X), Y), inverse(Y))
% 0.21/0.41 = { by lemma 3 R->L }
% 0.21/0.41 double_divide(multiply(inverse(X), Y), inverse(double_divide(multiply(inverse(X), Y), multiply(Z, multiply(inverse(Y), double_divide(multiply(inverse(X), Y), Z))))))
% 0.21/0.41 = { by axiom 1 (multiply) R->L }
% 0.21/0.41 double_divide(multiply(inverse(X), Y), multiply(multiply(Z, multiply(inverse(Y), double_divide(multiply(inverse(X), Y), Z))), multiply(inverse(X), Y)))
% 0.21/0.41 = { by lemma 3 R->L }
% 0.21/0.41 double_divide(multiply(inverse(X), Y), multiply(multiply(Z, multiply(inverse(Y), double_divide(multiply(inverse(X), Y), Z))), multiply(inverse(X), double_divide(multiply(inverse(X), Y), multiply(Z, multiply(inverse(Y), double_divide(multiply(inverse(X), Y), Z)))))))
% 0.21/0.41 = { by lemma 3 }
% 0.21/0.41 X
% 0.21/0.41
% 0.21/0.41 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.21/0.41 Proof:
% 0.21/0.41 multiply(multiply(inverse(b2), b2), a2)
% 0.21/0.41 = { by lemma 3 R->L }
% 0.21/0.41 double_divide(multiply(inverse(b2), b2), multiply(inverse(b2), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), double_divide(multiply(inverse(b2), b2), inverse(b2)))))
% 0.21/0.41 = { by lemma 4 }
% 0.21/0.41 double_divide(multiply(inverse(b2), b2), multiply(inverse(b2), multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), b2)))
% 0.21/0.41 = { by axiom 1 (multiply) }
% 0.21/0.41 double_divide(multiply(inverse(b2), b2), inverse(double_divide(multiply(inverse(multiply(multiply(inverse(b2), b2), a2)), b2), inverse(b2))))
% 0.21/0.41 = { by lemma 4 }
% 0.21/0.41 double_divide(multiply(inverse(b2), b2), inverse(multiply(multiply(inverse(b2), b2), a2)))
% 0.21/0.41 = { by axiom 1 (multiply) }
% 0.21/0.41 double_divide(inverse(double_divide(b2, inverse(b2))), inverse(multiply(multiply(inverse(b2), b2), a2)))
% 0.21/0.41 = { by lemma 4 R->L }
% 0.21/0.41 double_divide(inverse(double_divide(multiply(inverse(double_divide(b2, inverse(b2))), a2), inverse(a2))), inverse(multiply(multiply(inverse(b2), b2), a2)))
% 0.21/0.41 = { by axiom 1 (multiply) R->L }
% 0.21/0.41 double_divide(inverse(double_divide(multiply(multiply(inverse(b2), b2), a2), inverse(a2))), inverse(multiply(multiply(inverse(b2), b2), a2)))
% 0.21/0.41 = { by axiom 1 (multiply) R->L }
% 0.21/0.41 double_divide(multiply(inverse(a2), multiply(multiply(inverse(b2), b2), a2)), inverse(multiply(multiply(inverse(b2), b2), a2)))
% 0.21/0.41 = { by lemma 4 }
% 0.21/0.41 a2
% 0.21/0.41 % SZS output end Proof
% 0.21/0.41
% 0.21/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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