TSTP Solution File: GRP551-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP551-1 : 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 : n007.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 01:18:53 EDT 2023
% Result : Unsatisfiable 0.12s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GRP551-1 : TPTP v8.1.2. Released v2.6.0.
% 0.11/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Aug 28 22:26:28 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.39 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.12/0.39
% 0.12/0.39 % SZS status Unsatisfiable
% 0.12/0.39
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 Axiom 1 (identity): identity = divide(X, X).
% 0.12/0.40 Axiom 2 (inverse): inverse(X) = divide(identity, X).
% 0.12/0.40 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(identity, Y)).
% 0.12/0.40 Axiom 4 (single_axiom): divide(divide(identity, X), divide(divide(divide(Y, X), Z), Y)) = Z.
% 0.12/0.40
% 0.12/0.40 Lemma 5: divide(X, inverse(Y)) = multiply(X, Y).
% 0.12/0.40 Proof:
% 0.12/0.40 divide(X, inverse(Y))
% 0.12/0.40 = { by axiom 2 (inverse) }
% 0.12/0.40 divide(X, divide(identity, Y))
% 0.12/0.40 = { by axiom 3 (multiply) R->L }
% 0.12/0.40 multiply(X, Y)
% 0.12/0.40
% 0.12/0.40 Lemma 6: divide(X, identity) = multiply(X, identity).
% 0.12/0.40 Proof:
% 0.12/0.40 divide(X, identity)
% 0.12/0.40 = { by axiom 1 (identity) }
% 0.12/0.40 divide(X, divide(identity, identity))
% 0.12/0.40 = { by axiom 2 (inverse) R->L }
% 0.12/0.40 divide(X, inverse(identity))
% 0.12/0.40 = { by lemma 5 }
% 0.12/0.40 multiply(X, identity)
% 0.12/0.40
% 0.12/0.40 Lemma 7: divide(inverse(X), divide(divide(divide(Y, X), Z), Y)) = Z.
% 0.12/0.40 Proof:
% 0.12/0.40 divide(inverse(X), divide(divide(divide(Y, X), Z), Y))
% 0.12/0.40 = { by axiom 2 (inverse) }
% 0.12/0.40 divide(divide(identity, X), divide(divide(divide(Y, X), Z), Y))
% 0.12/0.40 = { by axiom 4 (single_axiom) }
% 0.12/0.41 Z
% 0.12/0.41
% 0.12/0.41 Lemma 8: multiply(inverse(X), Y) = divide(Y, X).
% 0.12/0.41 Proof:
% 0.12/0.41 multiply(inverse(X), Y)
% 0.12/0.41 = { by lemma 5 R->L }
% 0.12/0.41 divide(inverse(X), inverse(Y))
% 0.12/0.41 = { by axiom 2 (inverse) }
% 0.12/0.41 divide(inverse(X), divide(identity, Y))
% 0.12/0.41 = { by axiom 1 (identity) }
% 0.12/0.41 divide(inverse(X), divide(divide(divide(Y, X), divide(Y, X)), Y))
% 0.12/0.41 = { by lemma 7 }
% 0.12/0.41 divide(Y, X)
% 0.12/0.41
% 0.12/0.41 Lemma 9: divide(inverse(X), divide(inverse(Y), X)) = Y.
% 0.12/0.41 Proof:
% 0.12/0.41 divide(inverse(X), divide(inverse(Y), X))
% 0.12/0.41 = { by axiom 2 (inverse) }
% 0.12/0.41 divide(inverse(X), divide(divide(identity, Y), X))
% 0.12/0.41 = { by axiom 1 (identity) }
% 0.12/0.41 divide(inverse(X), divide(divide(divide(X, X), Y), X))
% 0.12/0.41 = { by lemma 7 }
% 0.12/0.41 Y
% 0.12/0.41
% 0.12/0.41 Lemma 10: inverse(inverse(X)) = X.
% 0.12/0.41 Proof:
% 0.12/0.41 inverse(inverse(X))
% 0.12/0.41 = { by axiom 2 (inverse) }
% 0.12/0.41 divide(identity, inverse(X))
% 0.12/0.41 = { by lemma 8 R->L }
% 0.12/0.41 multiply(inverse(inverse(X)), identity)
% 0.12/0.41 = { by lemma 6 R->L }
% 0.12/0.41 divide(inverse(inverse(X)), identity)
% 0.12/0.41 = { by axiom 1 (identity) }
% 0.19/0.41 divide(inverse(inverse(X)), divide(inverse(X), inverse(X)))
% 0.19/0.41 = { by lemma 9 }
% 0.19/0.41 X
% 0.19/0.41
% 0.19/0.41 Lemma 11: multiply(Y, X) = multiply(X, Y).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(Y, X)
% 0.19/0.41 = { by lemma 10 R->L }
% 0.19/0.41 multiply(inverse(inverse(Y)), X)
% 0.19/0.41 = { by lemma 8 }
% 0.19/0.41 divide(X, inverse(Y))
% 0.19/0.41 = { by lemma 5 }
% 0.19/0.41 multiply(X, Y)
% 0.19/0.41
% 0.19/0.41 Lemma 12: multiply(X, identity) = inverse(inverse(X)).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(X, identity)
% 0.19/0.41 = { by lemma 11 R->L }
% 0.19/0.41 multiply(identity, X)
% 0.19/0.41 = { by lemma 5 R->L }
% 0.19/0.41 divide(identity, inverse(X))
% 0.19/0.41 = { by axiom 2 (inverse) R->L }
% 0.19/0.41 inverse(inverse(X))
% 0.19/0.41
% 0.19/0.41 Lemma 13: divide(X, divide(X, Y)) = Y.
% 0.19/0.41 Proof:
% 0.19/0.41 divide(X, divide(X, Y))
% 0.19/0.41 = { by lemma 8 R->L }
% 0.19/0.41 divide(X, multiply(inverse(Y), X))
% 0.19/0.41 = { by lemma 5 R->L }
% 0.19/0.41 divide(X, divide(inverse(Y), inverse(X)))
% 0.19/0.41 = { by lemma 10 R->L }
% 0.19/0.41 divide(inverse(inverse(X)), divide(inverse(Y), inverse(X)))
% 0.19/0.41 = { by lemma 9 }
% 0.19/0.41 Y
% 0.19/0.41
% 0.19/0.41 Lemma 14: multiply(divide(X, Y), divide(Z, X)) = divide(Z, Y).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(divide(X, Y), divide(Z, X))
% 0.19/0.41 = { by lemma 13 R->L }
% 0.19/0.41 divide(Z, divide(Z, multiply(divide(X, Y), divide(Z, X))))
% 0.19/0.41 = { by lemma 11 }
% 0.19/0.41 divide(Z, divide(Z, multiply(divide(Z, X), divide(X, Y))))
% 0.19/0.41 = { by lemma 13 R->L }
% 0.19/0.41 divide(Z, divide(Z, multiply(divide(Z, X), divide(divide(Z, divide(Z, X)), Y))))
% 0.19/0.41 = { by lemma 11 }
% 0.19/0.41 divide(Z, divide(Z, multiply(divide(divide(Z, divide(Z, X)), Y), divide(Z, X))))
% 0.19/0.41 = { by lemma 8 R->L }
% 0.19/0.41 divide(Z, divide(Z, multiply(divide(multiply(inverse(divide(Z, X)), Z), Y), divide(Z, X))))
% 0.19/0.41 = { by lemma 5 R->L }
% 0.19/0.41 divide(Z, divide(Z, divide(divide(multiply(inverse(divide(Z, X)), Z), Y), inverse(divide(Z, X)))))
% 0.19/0.41 = { by lemma 5 R->L }
% 0.19/0.41 divide(Z, divide(Z, divide(divide(divide(inverse(divide(Z, X)), inverse(Z)), Y), inverse(divide(Z, X)))))
% 0.19/0.41 = { by lemma 10 R->L }
% 0.19/0.41 divide(Z, divide(inverse(inverse(Z)), divide(divide(divide(inverse(divide(Z, X)), inverse(Z)), Y), inverse(divide(Z, X)))))
% 0.19/0.41 = { by lemma 7 }
% 0.19/0.41 divide(Z, Y)
% 0.19/0.41
% 0.19/0.41 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.19/0.41 Proof:
% 0.19/0.41 multiply(multiply(a3, b3), c3)
% 0.19/0.41 = { by lemma 11 R->L }
% 0.19/0.41 multiply(c3, multiply(a3, b3))
% 0.19/0.41 = { by lemma 11 }
% 0.19/0.41 multiply(c3, multiply(b3, a3))
% 0.19/0.41 = { by lemma 11 }
% 0.19/0.41 multiply(multiply(b3, a3), c3)
% 0.19/0.41 = { by lemma 5 R->L }
% 0.19/0.41 divide(multiply(b3, a3), inverse(c3))
% 0.19/0.41 = { by lemma 14 R->L }
% 0.19/0.41 multiply(divide(b3, inverse(c3)), divide(multiply(b3, a3), b3))
% 0.19/0.41 = { by lemma 5 }
% 0.19/0.41 multiply(multiply(b3, c3), divide(multiply(b3, a3), b3))
% 0.19/0.41 = { by lemma 11 }
% 0.19/0.41 multiply(multiply(b3, c3), divide(multiply(a3, b3), b3))
% 0.19/0.41 = { by lemma 8 R->L }
% 0.19/0.41 multiply(multiply(b3, c3), multiply(inverse(b3), multiply(a3, b3)))
% 0.19/0.41 = { by lemma 5 R->L }
% 0.19/0.41 multiply(multiply(b3, c3), multiply(inverse(b3), divide(a3, inverse(b3))))
% 0.19/0.41 = { by lemma 11 }
% 0.19/0.41 multiply(multiply(b3, c3), multiply(divide(a3, inverse(b3)), inverse(b3)))
% 0.19/0.41 = { by lemma 5 R->L }
% 0.19/0.41 multiply(multiply(b3, c3), divide(divide(a3, inverse(b3)), inverse(inverse(b3))))
% 0.19/0.41 = { by lemma 8 R->L }
% 0.19/0.41 multiply(multiply(b3, c3), multiply(inverse(inverse(inverse(b3))), divide(a3, inverse(b3))))
% 0.19/0.41 = { by lemma 12 R->L }
% 0.19/0.41 multiply(multiply(b3, c3), multiply(multiply(inverse(b3), identity), divide(a3, inverse(b3))))
% 0.19/0.41 = { by lemma 6 R->L }
% 0.19/0.41 multiply(multiply(b3, c3), multiply(divide(inverse(b3), identity), divide(a3, inverse(b3))))
% 0.19/0.41 = { by lemma 14 }
% 0.19/0.41 multiply(multiply(b3, c3), divide(a3, identity))
% 0.19/0.41 = { by lemma 6 }
% 0.19/0.41 multiply(multiply(b3, c3), multiply(a3, identity))
% 0.19/0.41 = { by lemma 12 }
% 0.19/0.41 multiply(multiply(b3, c3), inverse(inverse(a3)))
% 0.19/0.41 = { by lemma 10 }
% 0.19/0.41 multiply(multiply(b3, c3), a3)
% 0.19/0.41 = { by lemma 11 R->L }
% 0.19/0.41 multiply(a3, multiply(b3, c3))
% 0.19/0.41 % SZS output end Proof
% 0.19/0.41
% 0.19/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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