TSTP Solution File: GRP462-1 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP462-1 : 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 : n020.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 01:18:32 EDT 2023
% Result : Unsatisfiable 0.20s 0.39s
% Output : Proof 0.20s
% 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 : GRP462-1 : 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
% 0.13/0.34 % Computer : n020.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 22:44:28 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.39 Command-line arguments: --no-flatten-goal
% 0.20/0.39
% 0.20/0.39 % SZS status Unsatisfiable
% 0.20/0.39
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Axiom 1 (identity): identity = divide(X, X).
% 0.20/0.41 Axiom 2 (inverse): inverse(X) = divide(identity, X).
% 0.20/0.41 Axiom 3 (multiply): multiply(X, Y) = divide(X, divide(identity, Y)).
% 0.20/0.41 Axiom 4 (single_axiom): divide(X, divide(divide(divide(identity, Y), Z), divide(divide(divide(X, X), X), Z))) = Y.
% 0.20/0.41
% 0.20/0.41 Lemma 5: inverse(identity) = identity.
% 0.20/0.41 Proof:
% 0.20/0.41 inverse(identity)
% 0.20/0.41 = { by axiom 2 (inverse) }
% 0.20/0.41 divide(identity, identity)
% 0.20/0.41 = { by axiom 1 (identity) R->L }
% 0.20/0.41 identity
% 0.20/0.41
% 0.20/0.41 Lemma 6: divide(X, divide(divide(inverse(Y), Z), divide(inverse(X), Z))) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 divide(X, divide(divide(inverse(Y), Z), divide(inverse(X), Z)))
% 0.20/0.41 = { by axiom 2 (inverse) }
% 0.20/0.41 divide(X, divide(divide(inverse(Y), Z), divide(divide(identity, X), Z)))
% 0.20/0.41 = { by axiom 1 (identity) }
% 0.20/0.41 divide(X, divide(divide(inverse(Y), Z), divide(divide(divide(X, X), X), Z)))
% 0.20/0.41 = { by axiom 2 (inverse) }
% 0.20/0.41 divide(X, divide(divide(divide(identity, Y), Z), divide(divide(divide(X, X), X), Z)))
% 0.20/0.41 = { by axiom 4 (single_axiom) }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 7: divide(X, identity) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 divide(X, identity)
% 0.20/0.41 = { by axiom 1 (identity) }
% 0.20/0.41 divide(X, divide(divide(inverse(X), Y), divide(inverse(X), Y)))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Lemma 8: divide(X, inverse(Y)) = multiply(X, Y).
% 0.20/0.41 Proof:
% 0.20/0.41 divide(X, inverse(Y))
% 0.20/0.41 = { by axiom 2 (inverse) }
% 0.20/0.41 divide(X, divide(identity, Y))
% 0.20/0.41 = { by axiom 3 (multiply) R->L }
% 0.20/0.41 multiply(X, Y)
% 0.20/0.41
% 0.20/0.41 Lemma 9: multiply(X, identity) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(X, identity)
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 divide(X, inverse(identity))
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 divide(X, identity)
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Lemma 10: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(X, multiply(inverse(X), Y))
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 multiply(X, divide(inverse(X), inverse(Y)))
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 divide(X, inverse(divide(inverse(X), inverse(Y))))
% 0.20/0.41 = { by axiom 2 (inverse) }
% 0.20/0.41 divide(X, divide(identity, divide(inverse(X), inverse(Y))))
% 0.20/0.41 = { by axiom 1 (identity) }
% 0.20/0.41 divide(X, divide(divide(inverse(Y), inverse(Y)), divide(inverse(X), inverse(Y))))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 11: inverse(inverse(X)) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 inverse(inverse(X))
% 0.20/0.41 = { by lemma 10 R->L }
% 0.20/0.41 multiply(X, multiply(inverse(X), inverse(inverse(X))))
% 0.20/0.41 = { by lemma 9 R->L }
% 0.20/0.41 multiply(X, multiply(inverse(X), multiply(inverse(inverse(X)), identity)))
% 0.20/0.41 = { by lemma 10 }
% 0.20/0.41 multiply(X, identity)
% 0.20/0.41 = { by lemma 9 }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Lemma 12: divide(X, multiply(inverse(Y), X)) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 divide(X, multiply(inverse(Y), X))
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 divide(X, divide(inverse(Y), inverse(X)))
% 0.20/0.41 = { by lemma 7 R->L }
% 0.20/0.41 divide(X, divide(inverse(Y), divide(inverse(X), identity)))
% 0.20/0.41 = { by lemma 7 R->L }
% 0.20/0.41 divide(X, divide(divide(inverse(Y), identity), divide(inverse(X), identity)))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 13: divide(X, multiply(Y, X)) = inverse(Y).
% 0.20/0.41 Proof:
% 0.20/0.41 divide(X, multiply(Y, X))
% 0.20/0.41 = { by lemma 11 R->L }
% 0.20/0.41 divide(X, multiply(inverse(inverse(Y)), X))
% 0.20/0.41 = { by lemma 12 }
% 0.20/0.41 inverse(Y)
% 0.20/0.41
% 0.20/0.41 Lemma 14: inverse(multiply(divide(inverse(X), Y), Y)) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 inverse(multiply(divide(inverse(X), Y), Y))
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 inverse(divide(divide(inverse(X), Y), inverse(Y)))
% 0.20/0.41 = { by axiom 2 (inverse) }
% 0.20/0.41 inverse(divide(divide(inverse(X), Y), divide(identity, Y)))
% 0.20/0.41 = { by axiom 2 (inverse) }
% 0.20/0.41 divide(identity, divide(divide(inverse(X), Y), divide(identity, Y)))
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 divide(identity, divide(divide(inverse(X), Y), divide(inverse(identity), Y)))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Lemma 15: multiply(divide(inverse(X), Y), Y) = inverse(X).
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(divide(inverse(X), Y), Y)
% 0.20/0.41 = { by lemma 12 R->L }
% 0.20/0.41 divide(Z, multiply(inverse(multiply(divide(inverse(X), Y), Y)), Z))
% 0.20/0.41 = { by lemma 14 }
% 0.20/0.41 divide(Z, multiply(X, Z))
% 0.20/0.41 = { by lemma 13 }
% 0.20/0.41 inverse(X)
% 0.20/0.41
% 0.20/0.41 Lemma 16: inverse(divide(X, Y)) = divide(Y, X).
% 0.20/0.41 Proof:
% 0.20/0.41 inverse(divide(X, Y))
% 0.20/0.41 = { by lemma 13 R->L }
% 0.20/0.41 divide(Y, multiply(divide(X, Y), Y))
% 0.20/0.41 = { by lemma 14 R->L }
% 0.20/0.41 divide(Y, multiply(divide(inverse(multiply(divide(inverse(X), Z), Z)), Y), Y))
% 0.20/0.41 = { by lemma 15 }
% 0.20/0.41 divide(Y, inverse(multiply(divide(inverse(X), Z), Z)))
% 0.20/0.41 = { by lemma 14 }
% 0.20/0.41 divide(Y, X)
% 0.20/0.41
% 0.20/0.41 Lemma 17: divide(inverse(X), Y) = inverse(multiply(Y, X)).
% 0.20/0.41 Proof:
% 0.20/0.41 divide(inverse(X), Y)
% 0.20/0.41 = { by lemma 16 R->L }
% 0.20/0.41 inverse(divide(Y, inverse(X)))
% 0.20/0.41 = { by lemma 8 }
% 0.20/0.41 inverse(multiply(Y, X))
% 0.20/0.41
% 0.20/0.41 Lemma 18: multiply(X, inverse(Y)) = divide(X, Y).
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(X, inverse(Y))
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 divide(X, inverse(inverse(Y)))
% 0.20/0.41 = { by lemma 11 }
% 0.20/0.41 divide(X, Y)
% 0.20/0.41
% 0.20/0.41 Lemma 19: divide(X, divide(Y, Z)) = multiply(X, divide(Z, Y)).
% 0.20/0.41 Proof:
% 0.20/0.41 divide(X, divide(Y, Z))
% 0.20/0.41 = { by lemma 16 R->L }
% 0.20/0.41 divide(X, inverse(divide(Z, Y)))
% 0.20/0.41 = { by lemma 8 }
% 0.20/0.41 multiply(X, divide(Z, Y))
% 0.20/0.41
% 0.20/0.41 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(multiply(a3, b3), c3)
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 divide(multiply(a3, b3), inverse(c3))
% 0.20/0.41 = { by lemma 16 R->L }
% 0.20/0.41 inverse(divide(inverse(c3), multiply(a3, b3)))
% 0.20/0.41 = { by lemma 18 R->L }
% 0.20/0.41 inverse(multiply(inverse(c3), inverse(multiply(a3, b3))))
% 0.20/0.42 = { by lemma 17 R->L }
% 0.20/0.42 inverse(multiply(inverse(c3), divide(inverse(b3), a3)))
% 0.20/0.42 = { by lemma 17 R->L }
% 0.20/0.42 divide(inverse(divide(inverse(b3), a3)), inverse(c3))
% 0.20/0.42 = { by lemma 6 R->L }
% 0.20/0.42 divide(a3, divide(divide(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3))), inverse(multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3)))), divide(inverse(a3), inverse(multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3))))))
% 0.20/0.42 = { by lemma 8 }
% 0.20/0.42 divide(a3, divide(multiply(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3))), multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3))), divide(inverse(a3), inverse(multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3))))))
% 0.20/0.42 = { by lemma 19 }
% 0.20/0.42 multiply(a3, divide(divide(inverse(a3), inverse(multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3)))), multiply(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3))), multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3)))))
% 0.20/0.42 = { by lemma 17 }
% 0.20/0.42 multiply(a3, divide(inverse(multiply(inverse(multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3))), a3)), multiply(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3))), multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3)))))
% 0.20/0.42 = { by lemma 17 }
% 0.20/0.42 multiply(a3, inverse(multiply(multiply(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3))), multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3))), multiply(inverse(multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3))), a3))))
% 0.20/0.42 = { by lemma 18 }
% 0.20/0.42 divide(a3, multiply(multiply(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3))), multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3))), multiply(inverse(multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3))), a3)))
% 0.20/0.42 = { by lemma 10 }
% 0.20/0.42 divide(a3, multiply(inverse(c3), multiply(inverse(multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3))), a3)))
% 0.20/0.42 = { by lemma 10 R->L }
% 0.20/0.42 divide(a3, multiply(inverse(c3), multiply(multiply(inverse(inverse(c3)), multiply(inverse(inverse(inverse(c3))), inverse(multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3))))), a3)))
% 0.20/0.42 = { by lemma 11 }
% 0.20/0.42 divide(a3, multiply(inverse(c3), multiply(multiply(inverse(inverse(c3)), multiply(inverse(c3), inverse(multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3))))), a3)))
% 0.20/0.42 = { by lemma 18 }
% 0.20/0.42 divide(a3, multiply(inverse(c3), multiply(multiply(inverse(inverse(c3)), divide(inverse(c3), multiply(inverse(inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), inverse(c3)))), a3)))
% 0.20/0.42 = { by lemma 12 }
% 0.20/0.42 divide(a3, multiply(inverse(c3), multiply(multiply(inverse(inverse(c3)), inverse(divide(inverse(divide(inverse(b3), a3)), inverse(c3)))), a3)))
% 0.20/0.42 = { by lemma 18 }
% 0.20/0.42 divide(a3, multiply(inverse(c3), multiply(divide(inverse(inverse(c3)), divide(inverse(divide(inverse(b3), a3)), inverse(c3))), a3)))
% 0.20/0.42 = { by lemma 17 }
% 0.20/0.42 divide(a3, multiply(inverse(c3), multiply(inverse(multiply(divide(inverse(divide(inverse(b3), a3)), inverse(c3)), inverse(c3))), a3)))
% 0.20/0.42 = { by lemma 14 }
% 0.20/0.42 divide(a3, multiply(inverse(c3), multiply(divide(inverse(b3), a3), a3)))
% 0.20/0.42 = { by lemma 15 }
% 0.20/0.42 divide(a3, multiply(inverse(c3), inverse(b3)))
% 0.20/0.42 = { by lemma 18 }
% 0.20/0.42 divide(a3, divide(inverse(c3), b3))
% 0.20/0.42 = { by lemma 19 }
% 0.20/0.42 multiply(a3, divide(b3, inverse(c3)))
% 0.20/0.42 = { by lemma 8 }
% 0.20/0.42 multiply(a3, multiply(b3, c3))
% 0.20/0.42 % SZS output end Proof
% 0.20/0.42
% 0.20/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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