TSTP Solution File: GRP456-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP456-1 : 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 : n027.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 0.40s
% 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
% 0.00/0.12 % Problem : GRP456-1 : 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
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Aug 29 00:00:52 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.14/0.40 Command-line arguments: --no-flatten-goal
% 0.14/0.40
% 0.14/0.40 % SZS status Unsatisfiable
% 0.14/0.40
% 0.14/0.42 % SZS output start Proof
% 0.14/0.42 Axiom 1 (identity): identity = divide(X, X).
% 0.14/0.42 Axiom 2 (inverse): inverse(X) = divide(identity, X).
% 0.14/0.42 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(identity, Y)).
% 0.14/0.42 Axiom 4 (single_axiom): divide(divide(identity, divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z) = Y.
% 0.14/0.42
% 0.14/0.42 Lemma 5: inverse(identity) = identity.
% 0.14/0.42 Proof:
% 0.14/0.42 inverse(identity)
% 0.14/0.42 = { by axiom 2 (inverse) }
% 0.14/0.42 divide(identity, identity)
% 0.14/0.42 = { by axiom 1 (identity) R->L }
% 0.14/0.42 identity
% 0.14/0.42
% 0.14/0.42 Lemma 6: divide(X, inverse(Y)) = multiply(X, Y).
% 0.14/0.42 Proof:
% 0.14/0.42 divide(X, inverse(Y))
% 0.14/0.42 = { by axiom 2 (inverse) }
% 0.14/0.42 divide(X, divide(identity, Y))
% 0.14/0.42 = { by axiom 3 (multiply) R->L }
% 0.14/0.42 multiply(X, Y)
% 0.14/0.42
% 0.14/0.42 Lemma 7: divide(X, identity) = multiply(X, identity).
% 0.14/0.42 Proof:
% 0.14/0.42 divide(X, identity)
% 0.14/0.42 = { by lemma 5 R->L }
% 0.14/0.42 divide(X, inverse(identity))
% 0.14/0.42 = { by lemma 6 }
% 0.14/0.42 multiply(X, identity)
% 0.14/0.42
% 0.14/0.42 Lemma 8: divide(inverse(divide(X, divide(Y, divide(inverse(X), Z)))), Z) = Y.
% 0.14/0.42 Proof:
% 0.14/0.42 divide(inverse(divide(X, divide(Y, divide(inverse(X), Z)))), Z)
% 0.14/0.42 = { by axiom 2 (inverse) }
% 0.14/0.42 divide(inverse(divide(X, divide(Y, divide(divide(identity, X), Z)))), Z)
% 0.14/0.42 = { by axiom 1 (identity) }
% 0.14/0.42 divide(inverse(divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z)
% 0.14/0.42 = { by axiom 2 (inverse) }
% 0.14/0.42 divide(divide(identity, divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z)
% 0.14/0.42 = { by axiom 4 (single_axiom) }
% 0.14/0.42 Y
% 0.14/0.42
% 0.14/0.42 Lemma 9: divide(inverse(inverse(multiply(X, Y))), Y) = X.
% 0.14/0.42 Proof:
% 0.14/0.42 divide(inverse(inverse(multiply(X, Y))), Y)
% 0.14/0.42 = { by lemma 6 R->L }
% 0.14/0.42 divide(inverse(inverse(divide(X, inverse(Y)))), Y)
% 0.14/0.42 = { by axiom 2 (inverse) }
% 0.14/0.42 divide(inverse(inverse(divide(X, divide(identity, Y)))), Y)
% 0.14/0.42 = { by axiom 2 (inverse) }
% 0.14/0.42 divide(inverse(divide(identity, divide(X, divide(identity, Y)))), Y)
% 0.14/0.42 = { by lemma 5 R->L }
% 0.14/0.42 divide(inverse(divide(identity, divide(X, divide(inverse(identity), Y)))), Y)
% 0.14/0.42 = { by lemma 8 }
% 0.14/0.42 X
% 0.14/0.42
% 0.14/0.42 Lemma 10: inverse(multiply(X, identity)) = inverse(X).
% 0.14/0.42 Proof:
% 0.14/0.42 inverse(multiply(X, identity))
% 0.14/0.42 = { by lemma 8 R->L }
% 0.14/0.42 divide(inverse(divide(Y, divide(inverse(multiply(X, identity)), divide(inverse(Y), Z)))), Z)
% 0.14/0.42 = { by lemma 7 R->L }
% 0.14/0.42 divide(inverse(divide(Y, divide(inverse(divide(X, identity)), divide(inverse(Y), Z)))), Z)
% 0.14/0.42 = { by axiom 1 (identity) }
% 0.14/0.42 divide(inverse(divide(Y, divide(inverse(divide(X, divide(divide(inverse(X), divide(inverse(Y), Z)), divide(inverse(X), divide(inverse(Y), Z))))), divide(inverse(Y), Z)))), Z)
% 0.14/0.42 = { by lemma 8 }
% 0.14/0.42 divide(inverse(divide(Y, divide(inverse(X), divide(inverse(Y), Z)))), Z)
% 0.14/0.42 = { by lemma 8 }
% 0.14/0.42 inverse(X)
% 0.14/0.42
% 0.14/0.42 Lemma 11: multiply(inverse(inverse(X)), identity) = X.
% 0.14/0.42 Proof:
% 0.14/0.42 multiply(inverse(inverse(X)), identity)
% 0.14/0.42 = { by lemma 10 R->L }
% 0.14/0.42 multiply(inverse(inverse(multiply(X, identity))), identity)
% 0.14/0.42 = { by lemma 7 R->L }
% 0.14/0.42 divide(inverse(inverse(multiply(X, identity))), identity)
% 0.14/0.42 = { by lemma 9 }
% 0.14/0.42 X
% 0.14/0.42
% 0.14/0.42 Lemma 12: inverse(inverse(X)) = X.
% 0.14/0.42 Proof:
% 0.14/0.42 inverse(inverse(X))
% 0.14/0.42 = { by lemma 9 R->L }
% 0.14/0.42 divide(inverse(inverse(multiply(inverse(inverse(X)), identity))), identity)
% 0.14/0.42 = { by lemma 11 }
% 0.14/0.42 divide(inverse(inverse(X)), identity)
% 0.14/0.42 = { by lemma 7 }
% 0.14/0.42 multiply(inverse(inverse(X)), identity)
% 0.14/0.42 = { by lemma 11 }
% 0.14/0.42 X
% 0.14/0.42
% 0.14/0.42 Lemma 13: multiply(X, inverse(Y)) = divide(X, Y).
% 0.14/0.42 Proof:
% 0.14/0.42 multiply(X, inverse(Y))
% 0.14/0.42 = { by lemma 6 R->L }
% 0.14/0.42 divide(X, inverse(inverse(Y)))
% 0.14/0.42 = { by lemma 12 }
% 0.14/0.42 divide(X, Y)
% 0.14/0.42
% 0.14/0.42 Lemma 14: inverse(divide(X, Y)) = divide(Y, X).
% 0.14/0.42 Proof:
% 0.14/0.42 inverse(divide(X, Y))
% 0.14/0.42 = { by lemma 9 R->L }
% 0.14/0.42 divide(inverse(inverse(multiply(inverse(divide(X, Y)), X))), X)
% 0.14/0.42 = { by lemma 11 R->L }
% 0.14/0.42 divide(inverse(inverse(multiply(inverse(divide(X, multiply(inverse(inverse(Y)), identity))), X))), X)
% 0.14/0.42 = { by lemma 10 R->L }
% 0.14/0.42 divide(inverse(inverse(multiply(inverse(divide(X, multiply(inverse(inverse(multiply(Y, identity))), identity))), X))), X)
% 0.14/0.42 = { by lemma 11 }
% 0.14/0.42 divide(inverse(inverse(multiply(inverse(divide(X, multiply(Y, identity))), X))), X)
% 0.14/0.42 = { by lemma 7 R->L }
% 0.14/0.42 divide(inverse(inverse(multiply(inverse(divide(X, divide(Y, identity))), X))), X)
% 0.14/0.42 = { by lemma 6 R->L }
% 0.14/0.42 divide(inverse(inverse(divide(inverse(divide(X, divide(Y, identity))), inverse(X)))), X)
% 0.14/0.42 = { by axiom 1 (identity) }
% 0.14/0.42 divide(inverse(inverse(divide(inverse(divide(X, divide(Y, divide(inverse(X), inverse(X))))), inverse(X)))), X)
% 0.14/0.42 = { by lemma 8 }
% 0.14/0.42 divide(inverse(inverse(Y)), X)
% 0.14/0.42 = { by lemma 12 }
% 0.14/0.42 divide(Y, X)
% 0.14/0.42
% 0.14/0.42 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.14/0.42 Proof:
% 0.14/0.42 multiply(multiply(a3, b3), c3)
% 0.14/0.42 = { by lemma 6 R->L }
% 0.14/0.42 divide(multiply(a3, b3), inverse(c3))
% 0.14/0.42 = { by lemma 6 R->L }
% 0.14/0.42 divide(divide(a3, inverse(b3)), inverse(c3))
% 0.14/0.42 = { by lemma 14 R->L }
% 0.14/0.42 divide(inverse(divide(inverse(b3), a3)), inverse(c3))
% 0.14/0.42 = { by lemma 9 R->L }
% 0.14/0.42 divide(inverse(divide(inverse(b3), divide(inverse(inverse(multiply(a3, divide(inverse(inverse(b3)), inverse(c3))))), divide(inverse(inverse(b3)), inverse(c3))))), inverse(c3))
% 0.14/0.42 = { by lemma 12 }
% 0.14/0.42 divide(inverse(divide(inverse(b3), divide(multiply(a3, divide(inverse(inverse(b3)), inverse(c3))), divide(inverse(inverse(b3)), inverse(c3))))), inverse(c3))
% 0.14/0.42 = { by lemma 8 }
% 0.14/0.42 multiply(a3, divide(inverse(inverse(b3)), inverse(c3)))
% 0.14/0.42 = { by lemma 14 R->L }
% 0.14/0.42 multiply(a3, inverse(divide(inverse(c3), inverse(inverse(b3)))))
% 0.14/0.42 = { by lemma 6 }
% 0.14/0.42 multiply(a3, inverse(multiply(inverse(c3), inverse(b3))))
% 0.14/0.42 = { by lemma 13 }
% 0.14/0.42 divide(a3, multiply(inverse(c3), inverse(b3)))
% 0.14/0.42 = { by lemma 13 }
% 0.14/0.42 divide(a3, divide(inverse(c3), b3))
% 0.14/0.42 = { by lemma 14 R->L }
% 0.14/0.42 divide(a3, inverse(divide(b3, inverse(c3))))
% 0.14/0.42 = { by lemma 6 }
% 0.14/0.42 multiply(a3, divide(b3, inverse(c3)))
% 0.14/0.42 = { by lemma 6 }
% 0.14/0.42 multiply(a3, multiply(b3, c3))
% 0.14/0.42 % SZS output end Proof
% 0.14/0.42
% 0.14/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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