TSTP Solution File: GRP453-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP453-1 : 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 : n026.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 01:18:29 EDT 2023
% Result : Unsatisfiable 0.19s 0.41s
% 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
% 0.00/0.12 % Problem : GRP453-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.15/0.34 % Computer : n026.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Mon Aug 28 20:11:35 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.19/0.41 Command-line arguments: --no-flatten-goal
% 0.19/0.41
% 0.19/0.41 % SZS status Unsatisfiable
% 0.19/0.41
% 0.19/0.43 % SZS output start Proof
% 0.19/0.43 Axiom 1 (inverse): inverse(X) = divide(divide(Y, Y), X).
% 0.19/0.43 Axiom 2 (multiply): multiply(X, Y) = divide(X, divide(divide(Z, Z), Y)).
% 0.19/0.43 Axiom 3 (single_axiom): divide(divide(divide(X, X), divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z) = Y.
% 0.19/0.43
% 0.19/0.43 Lemma 4: divide(X, inverse(Y)) = multiply(X, Y).
% 0.19/0.43 Proof:
% 0.19/0.43 divide(X, inverse(Y))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 divide(X, divide(divide(Z, Z), Y))
% 0.19/0.43 = { by axiom 2 (multiply) R->L }
% 0.19/0.43 multiply(X, Y)
% 0.19/0.43
% 0.19/0.43 Lemma 5: divide(inverse(divide(X, X)), Y) = inverse(Y).
% 0.19/0.43 Proof:
% 0.19/0.43 divide(inverse(divide(X, X)), Y)
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 divide(divide(divide(X, X), divide(X, X)), Y)
% 0.19/0.43 = { by axiom 1 (inverse) R->L }
% 0.19/0.43 inverse(Y)
% 0.19/0.43
% 0.19/0.43 Lemma 6: divide(inverse(divide(X, divide(Y, divide(inverse(X), Z)))), Z) = Y.
% 0.19/0.43 Proof:
% 0.19/0.43 divide(inverse(divide(X, divide(Y, divide(inverse(X), Z)))), Z)
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 divide(inverse(divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z)
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 divide(divide(divide(X, X), divide(X, divide(Y, divide(divide(divide(X, X), X), Z)))), Z)
% 0.19/0.43 = { by axiom 3 (single_axiom) }
% 0.19/0.43 Y
% 0.19/0.43
% 0.19/0.43 Lemma 7: divide(inverse(inverse(multiply(X, Y))), Y) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 divide(inverse(inverse(multiply(X, Y))), Y)
% 0.19/0.43 = { by lemma 4 R->L }
% 0.19/0.43 divide(inverse(inverse(divide(X, inverse(Y)))), Y)
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 divide(inverse(divide(divide(Z, Z), divide(X, inverse(Y)))), Y)
% 0.19/0.43 = { by lemma 5 R->L }
% 0.19/0.43 divide(inverse(divide(divide(Z, Z), divide(X, divide(inverse(divide(Z, Z)), Y)))), Y)
% 0.19/0.43 = { by lemma 6 }
% 0.19/0.43 X
% 0.19/0.43
% 0.19/0.43 Lemma 8: multiply(divide(X, X), Y) = inverse(inverse(Y)).
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(divide(X, X), Y)
% 0.19/0.43 = { by lemma 4 R->L }
% 0.19/0.43 divide(divide(X, X), inverse(Y))
% 0.19/0.43 = { by axiom 1 (inverse) R->L }
% 0.19/0.43 inverse(inverse(Y))
% 0.19/0.43
% 0.19/0.43 Lemma 9: divide(Y, Y) = divide(X, X).
% 0.19/0.43 Proof:
% 0.19/0.43 divide(Y, Y)
% 0.19/0.43 = { by lemma 7 R->L }
% 0.19/0.43 divide(inverse(inverse(multiply(divide(Y, Y), Z))), Z)
% 0.19/0.43 = { by lemma 8 }
% 0.19/0.43 divide(inverse(inverse(inverse(inverse(Z)))), Z)
% 0.19/0.43 = { by lemma 8 R->L }
% 0.19/0.43 divide(inverse(inverse(multiply(divide(X, X), Z))), Z)
% 0.19/0.43 = { by lemma 7 }
% 0.19/0.43 divide(X, X)
% 0.19/0.43
% 0.19/0.43 Lemma 10: multiply(inverse(inverse(multiply(X, inverse(Y)))), Y) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(inverse(inverse(multiply(X, inverse(Y)))), Y)
% 0.19/0.43 = { by lemma 4 R->L }
% 0.19/0.43 divide(inverse(inverse(multiply(X, inverse(Y)))), inverse(Y))
% 0.19/0.43 = { by lemma 7 }
% 0.19/0.43 X
% 0.19/0.43
% 0.19/0.43 Lemma 11: multiply(divide(inverse(inverse(X)), Y), Y) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(divide(inverse(inverse(X)), Y), Y)
% 0.19/0.43 = { by lemma 10 R->L }
% 0.19/0.43 multiply(divide(inverse(inverse(multiply(inverse(inverse(multiply(X, inverse(Y)))), Y))), Y), Y)
% 0.19/0.43 = { by lemma 7 }
% 0.19/0.43 multiply(inverse(inverse(multiply(X, inverse(Y)))), Y)
% 0.19/0.43 = { by lemma 4 R->L }
% 0.19/0.43 divide(inverse(inverse(multiply(X, inverse(Y)))), inverse(Y))
% 0.19/0.43 = { by lemma 7 }
% 0.19/0.43 X
% 0.19/0.43
% 0.19/0.43 Lemma 12: inverse(divide(X, X)) = divide(Y, Y).
% 0.19/0.43 Proof:
% 0.19/0.43 inverse(divide(X, X))
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 divide(divide(X, X), divide(X, X))
% 0.19/0.43 = { by lemma 9 R->L }
% 0.19/0.43 divide(Y, Y)
% 0.19/0.43
% 0.19/0.43 Lemma 13: multiply(X, multiply(inverse(X), Y)) = Y.
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(X, multiply(inverse(X), Y))
% 0.19/0.43 = { by lemma 11 R->L }
% 0.19/0.43 multiply(divide(inverse(inverse(multiply(X, multiply(inverse(X), Y)))), Z), Z)
% 0.19/0.43 = { by lemma 7 R->L }
% 0.19/0.43 multiply(divide(inverse(divide(inverse(inverse(multiply(inverse(multiply(X, multiply(inverse(X), Y))), Y))), Y)), Z), Z)
% 0.19/0.43 = { by lemma 4 R->L }
% 0.19/0.43 multiply(divide(inverse(divide(inverse(inverse(multiply(inverse(multiply(X, divide(inverse(X), inverse(Y)))), Y))), Y)), Z), Z)
% 0.19/0.43 = { by lemma 4 R->L }
% 0.19/0.43 multiply(divide(inverse(divide(inverse(inverse(divide(inverse(multiply(X, divide(inverse(X), inverse(Y)))), inverse(Y)))), Y)), Z), Z)
% 0.19/0.43 = { by lemma 4 R->L }
% 0.19/0.43 multiply(divide(inverse(divide(inverse(inverse(divide(inverse(divide(X, inverse(divide(inverse(X), inverse(Y))))), inverse(Y)))), Y)), Z), Z)
% 0.19/0.43 = { by axiom 1 (inverse) }
% 0.19/0.43 multiply(divide(inverse(divide(inverse(inverse(divide(inverse(divide(X, divide(divide(W, W), divide(inverse(X), inverse(Y))))), inverse(Y)))), Y)), Z), Z)
% 0.19/0.43 = { by lemma 6 }
% 0.19/0.43 multiply(divide(inverse(divide(inverse(inverse(divide(W, W))), Y)), Z), Z)
% 0.19/0.43 = { by lemma 12 }
% 0.19/0.43 multiply(divide(inverse(divide(inverse(divide(V, V)), Y)), Z), Z)
% 0.19/0.43 = { by lemma 5 }
% 0.19/0.43 multiply(divide(inverse(inverse(Y)), Z), Z)
% 0.19/0.43 = { by lemma 11 }
% 0.19/0.43 Y
% 0.19/0.43
% 0.19/0.43 Lemma 14: multiply(X, divide(Y, Y)) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(X, divide(Y, Y))
% 0.19/0.43 = { by lemma 9 }
% 0.19/0.43 multiply(X, divide(inverse(X), inverse(X)))
% 0.19/0.43 = { by lemma 4 }
% 0.19/0.43 multiply(X, multiply(inverse(X), X))
% 0.19/0.43 = { by lemma 13 }
% 0.19/0.43 X
% 0.19/0.43
% 0.19/0.43 Lemma 15: inverse(inverse(X)) = X.
% 0.19/0.43 Proof:
% 0.19/0.43 inverse(inverse(X))
% 0.19/0.43 = { by lemma 14 R->L }
% 0.19/0.43 multiply(inverse(inverse(X)), divide(Y, Y))
% 0.19/0.43 = { by lemma 4 R->L }
% 0.19/0.43 divide(inverse(inverse(X)), inverse(divide(Y, Y)))
% 0.19/0.43 = { by lemma 12 }
% 0.19/0.43 divide(inverse(inverse(X)), divide(Z, Z))
% 0.19/0.43 = { by lemma 14 R->L }
% 0.19/0.43 divide(inverse(inverse(multiply(X, divide(Z, Z)))), divide(Z, Z))
% 0.19/0.43 = { by lemma 7 }
% 0.19/0.43 X
% 0.19/0.43
% 0.19/0.43 Lemma 16: multiply(X, inverse(Y)) = divide(X, Y).
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(X, inverse(Y))
% 0.19/0.43 = { by lemma 4 R->L }
% 0.19/0.43 divide(X, inverse(inverse(Y)))
% 0.19/0.43 = { by lemma 15 }
% 0.19/0.43 divide(X, Y)
% 0.19/0.43
% 0.19/0.43 Lemma 17: inverse(divide(X, Y)) = divide(Y, X).
% 0.19/0.43 Proof:
% 0.19/0.43 inverse(divide(X, Y))
% 0.19/0.43 = { by lemma 7 R->L }
% 0.19/0.43 divide(inverse(inverse(multiply(inverse(divide(X, Y)), X))), X)
% 0.19/0.43 = { by lemma 16 R->L }
% 0.19/0.43 divide(inverse(inverse(multiply(inverse(multiply(X, inverse(Y))), X))), X)
% 0.19/0.43 = { by lemma 10 R->L }
% 0.19/0.43 divide(inverse(inverse(multiply(inverse(multiply(X, inverse(Y))), multiply(inverse(inverse(multiply(X, inverse(Y)))), Y)))), X)
% 0.19/0.43 = { by lemma 13 }
% 0.19/0.43 divide(inverse(inverse(Y)), X)
% 0.19/0.43 = { by lemma 15 }
% 0.19/0.43 divide(Y, X)
% 0.19/0.43
% 0.19/0.43 Lemma 18: divide(inverse(X), Y) = inverse(multiply(Y, X)).
% 0.19/0.43 Proof:
% 0.19/0.43 divide(inverse(X), Y)
% 0.19/0.43 = { by lemma 17 R->L }
% 0.19/0.43 inverse(divide(Y, inverse(X)))
% 0.19/0.43 = { by lemma 4 }
% 0.19/0.43 inverse(multiply(Y, X))
% 0.19/0.43
% 0.19/0.43 Goal 1 (prove_these_axioms_3): multiply(multiply(a3, b3), c3) = multiply(a3, multiply(b3, c3)).
% 0.19/0.43 Proof:
% 0.19/0.43 multiply(multiply(a3, b3), c3)
% 0.19/0.43 = { by lemma 4 R->L }
% 0.19/0.43 divide(multiply(a3, b3), inverse(c3))
% 0.19/0.43 = { by lemma 17 R->L }
% 0.19/0.43 inverse(divide(inverse(c3), multiply(a3, b3)))
% 0.19/0.43 = { by lemma 15 R->L }
% 0.19/0.43 inverse(inverse(inverse(divide(inverse(c3), multiply(a3, b3)))))
% 0.19/0.43 = { by lemma 11 R->L }
% 0.19/0.43 multiply(divide(inverse(inverse(inverse(inverse(inverse(divide(inverse(c3), multiply(a3, b3))))))), X), X)
% 0.19/0.43 = { by lemma 8 R->L }
% 0.19/0.43 multiply(divide(multiply(divide(inverse(inverse(inverse(divide(inverse(c3), multiply(a3, b3))))), inverse(inverse(inverse(divide(inverse(c3), multiply(a3, b3)))))), inverse(inverse(inverse(divide(inverse(c3), multiply(a3, b3)))))), X), X)
% 0.19/0.43 = { by lemma 11 }
% 0.19/0.43 multiply(divide(inverse(divide(inverse(c3), multiply(a3, b3))), X), X)
% 0.19/0.43 = { by lemma 16 R->L }
% 0.19/0.43 multiply(divide(inverse(multiply(inverse(c3), inverse(multiply(a3, b3)))), X), X)
% 0.19/0.43 = { by lemma 18 R->L }
% 0.19/0.43 multiply(divide(inverse(multiply(inverse(c3), divide(inverse(b3), a3))), X), X)
% 0.19/0.43 = { by lemma 15 R->L }
% 0.19/0.43 multiply(divide(inverse(inverse(inverse(multiply(inverse(c3), divide(inverse(b3), a3))))), X), X)
% 0.19/0.43 = { by lemma 6 R->L }
% 0.19/0.43 multiply(divide(inverse(divide(inverse(divide(b3, divide(inverse(inverse(multiply(inverse(c3), divide(inverse(b3), a3)))), divide(inverse(b3), a3)))), a3)), X), X)
% 0.19/0.43 = { by lemma 7 }
% 0.19/0.43 multiply(divide(inverse(divide(inverse(divide(b3, inverse(c3))), a3)), X), X)
% 0.19/0.43 = { by lemma 18 }
% 0.19/0.43 multiply(divide(inverse(inverse(multiply(a3, divide(b3, inverse(c3))))), X), X)
% 0.19/0.43 = { by lemma 11 }
% 0.19/0.43 multiply(a3, divide(b3, inverse(c3)))
% 0.19/0.43 = { by lemma 4 }
% 0.19/0.43 multiply(a3, multiply(b3, c3))
% 0.19/0.43 % SZS output end Proof
% 0.19/0.43
% 0.19/0.43 RESULT: Unsatisfiable (the axioms are contradictory).
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