TSTP Solution File: GRP455-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP455-1 : 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 : n019.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 01:18:30 EDT 2023
% Result : Unsatisfiable 0.14s 0.33s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GRP455-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.09/0.30 % Computer : n019.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Aug 28 20:45:43 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.14/0.33 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.14/0.33
% 0.14/0.33 % SZS status Unsatisfiable
% 0.14/0.33
% 0.14/0.34 % SZS output start Proof
% 0.14/0.34 Axiom 1 (identity): identity = divide(X, X).
% 0.14/0.34 Axiom 2 (inverse): inverse(X) = divide(identity, X).
% 0.14/0.34 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(identity, Y)).
% 0.14/0.34 Axiom 4 (single_axiom): divide(divide(identity, divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z) = Y.
% 0.14/0.34
% 0.14/0.34 Lemma 5: inverse(identity) = identity.
% 0.14/0.34 Proof:
% 0.14/0.34 inverse(identity)
% 0.14/0.34 = { by axiom 2 (inverse) }
% 0.14/0.34 divide(identity, identity)
% 0.14/0.34 = { by axiom 1 (identity) R->L }
% 0.14/0.34 identity
% 0.14/0.34
% 0.14/0.34 Lemma 6: divide(X, inverse(Y)) = multiply(X, Y).
% 0.14/0.34 Proof:
% 0.14/0.34 divide(X, inverse(Y))
% 0.14/0.34 = { by axiom 2 (inverse) }
% 0.14/0.34 divide(X, divide(identity, Y))
% 0.14/0.34 = { by axiom 3 (multiply) R->L }
% 0.14/0.34 multiply(X, Y)
% 0.14/0.34
% 0.14/0.34 Lemma 7: multiply(identity, X) = inverse(inverse(X)).
% 0.14/0.34 Proof:
% 0.14/0.34 multiply(identity, X)
% 0.14/0.34 = { by lemma 6 R->L }
% 0.14/0.34 divide(identity, inverse(X))
% 0.14/0.34 = { by axiom 2 (inverse) R->L }
% 0.14/0.34 inverse(inverse(X))
% 0.14/0.34
% 0.14/0.34 Lemma 8: multiply(inverse(divide(X, multiply(Y, identity))), X) = Y.
% 0.14/0.34 Proof:
% 0.14/0.34 multiply(inverse(divide(X, multiply(Y, identity))), X)
% 0.14/0.34 = { by lemma 6 R->L }
% 0.14/0.34 multiply(inverse(divide(X, divide(Y, inverse(identity)))), X)
% 0.14/0.34 = { by lemma 5 }
% 0.14/0.34 multiply(inverse(divide(X, divide(Y, identity))), X)
% 0.14/0.34 = { by lemma 6 R->L }
% 0.14/0.34 divide(inverse(divide(X, divide(Y, identity))), inverse(X))
% 0.14/0.34 = { by axiom 1 (identity) }
% 0.14/0.34 divide(inverse(divide(X, divide(Y, divide(inverse(X), inverse(X))))), inverse(X))
% 0.14/0.34 = { by axiom 2 (inverse) }
% 0.14/0.34 divide(inverse(divide(X, divide(Y, divide(divide(identity, X), inverse(X))))), inverse(X))
% 0.14/0.34 = { by axiom 1 (identity) }
% 0.14/0.34 divide(inverse(divide(X, divide(Y, divide(divide(divide(X, X), X), inverse(X))))), inverse(X))
% 0.14/0.34 = { by axiom 2 (inverse) }
% 0.14/0.34 divide(divide(identity, divide(X, divide(Y, divide(divide(divide(X, X), X), inverse(X))))), inverse(X))
% 0.14/0.34 = { by axiom 4 (single_axiom) }
% 0.14/0.34 Y
% 0.14/0.34
% 0.14/0.34 Lemma 9: inverse(inverse(multiply(X, identity))) = X.
% 0.14/0.34 Proof:
% 0.14/0.34 inverse(inverse(multiply(X, identity)))
% 0.14/0.34 = { by lemma 7 R->L }
% 0.14/0.34 multiply(identity, multiply(X, identity))
% 0.14/0.34 = { by lemma 5 R->L }
% 0.14/0.34 multiply(inverse(identity), multiply(X, identity))
% 0.14/0.34 = { by axiom 1 (identity) }
% 0.14/0.34 multiply(inverse(divide(multiply(X, identity), multiply(X, identity))), multiply(X, identity))
% 0.14/0.34 = { by lemma 8 }
% 0.14/0.34 X
% 0.14/0.34
% 0.14/0.34 Goal 1 (prove_these_axioms_2): multiply(identity, a2) = a2.
% 0.14/0.34 Proof:
% 0.14/0.34 multiply(identity, a2)
% 0.14/0.34 = { by lemma 7 }
% 0.14/0.34 inverse(inverse(a2))
% 0.14/0.34 = { by lemma 8 R->L }
% 0.14/0.34 inverse(inverse(multiply(inverse(divide(identity, multiply(a2, identity))), identity)))
% 0.14/0.34 = { by lemma 9 }
% 0.14/0.34 inverse(divide(identity, multiply(a2, identity)))
% 0.14/0.34 = { by axiom 2 (inverse) R->L }
% 0.14/0.34 inverse(inverse(multiply(a2, identity)))
% 0.14/0.34 = { by lemma 9 }
% 0.14/0.34 a2
% 0.14/0.34 % SZS output end Proof
% 0.14/0.34
% 0.14/0.34 RESULT: Unsatisfiable (the axioms are contradictory).
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