TSTP Solution File: GRP563-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP563-1 : 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 : n012.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 01:18:55 EDT 2023
% Result : Unsatisfiable 0.20s 0.40s
% 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
% 0.00/0.12 % Problem : GRP563-1 : 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
% 0.13/0.34 % Computer : n012.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 22:10:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.40 Command-line arguments: --no-flatten-goal
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% 0.20/0.40 % SZS status Unsatisfiable
% 0.20/0.40
% 0.20/0.41 % SZS output start Proof
% 0.20/0.41 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.20/0.41 Axiom 2 (single_axiom): divide(divide(divide(X, inverse(Y)), Z), divide(X, Z)) = Y.
% 0.20/0.41
% 0.20/0.41 Lemma 3: divide(divide(multiply(X, Y), Z), divide(X, Z)) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 divide(divide(multiply(X, Y), Z), divide(X, Z))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 divide(divide(divide(X, inverse(Y)), Z), divide(X, Z))
% 0.20/0.41 = { by axiom 2 (single_axiom) }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 4: divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), Y) = W.
% 0.20/0.41 Proof:
% 0.20/0.41 divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), Y)
% 0.20/0.41 = { by lemma 3 R->L }
% 0.20/0.41 divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), divide(divide(multiply(X, Y), Z), divide(X, Z)))
% 0.20/0.41 = { by lemma 3 }
% 0.20/0.41 W
% 0.20/0.41
% 0.20/0.41 Lemma 5: multiply(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), Y) = W.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), Y)
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 divide(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), inverse(Y))
% 0.20/0.41 = { by lemma 4 }
% 0.20/0.41 W
% 0.20/0.41
% 0.20/0.41 Lemma 6: divide(multiply(X, Y), X) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 divide(multiply(X, Y), X)
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 divide(divide(X, inverse(Y)), X)
% 0.20/0.41 = { by lemma 3 R->L }
% 0.20/0.41 divide(divide(X, divide(divide(multiply(Z, inverse(Y)), W), divide(Z, W))), X)
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 divide(divide(multiply(divide(multiply(divide(multiply(Z, inverse(Y)), W), X), divide(Z, W)), Y), divide(divide(multiply(Z, inverse(Y)), W), divide(Z, W))), X)
% 0.20/0.41 = { by lemma 4 }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 7: divide(multiply(multiply(X, Y), Z), multiply(X, Z)) = Y.
% 0.20/0.41 Proof:
% 0.20/0.41 divide(multiply(multiply(X, Y), Z), multiply(X, Z))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 divide(multiply(multiply(X, Y), Z), divide(X, inverse(Z)))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 divide(divide(multiply(X, Y), inverse(Z)), divide(X, inverse(Z)))
% 0.20/0.41 = { by lemma 3 }
% 0.20/0.41 Y
% 0.20/0.41
% 0.20/0.41 Lemma 8: multiply(divide(X, Y), Y) = X.
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(divide(X, Y), Y)
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 divide(divide(X, Y), inverse(Y))
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 divide(divide(X, divide(multiply(multiply(inverse(Y), multiply(inverse(Y), X)), Y), multiply(inverse(Y), multiply(inverse(Y), X)))), inverse(Y))
% 0.20/0.41 = { by axiom 1 (multiply) }
% 0.20/0.41 divide(divide(X, divide(multiply(divide(inverse(Y), inverse(multiply(inverse(Y), X))), Y), multiply(inverse(Y), multiply(inverse(Y), X)))), inverse(Y))
% 0.20/0.41 = { by lemma 3 R->L }
% 0.20/0.41 divide(divide(X, divide(multiply(divide(inverse(Y), divide(divide(multiply(Z, inverse(multiply(inverse(Y), X))), W), divide(Z, W))), Y), multiply(inverse(Y), multiply(inverse(Y), X)))), inverse(Y))
% 0.20/0.41 = { by lemma 5 R->L }
% 0.20/0.41 divide(divide(X, divide(multiply(divide(multiply(divide(multiply(divide(multiply(Z, inverse(multiply(inverse(Y), X))), W), inverse(Y)), divide(Z, W)), multiply(inverse(Y), X)), divide(divide(multiply(Z, inverse(multiply(inverse(Y), X))), W), divide(Z, W))), Y), multiply(inverse(Y), multiply(inverse(Y), X)))), inverse(Y))
% 0.20/0.41 = { by lemma 5 }
% 0.20/0.41 divide(divide(X, divide(multiply(inverse(Y), X), multiply(inverse(Y), multiply(inverse(Y), X)))), inverse(Y))
% 0.20/0.41 = { by lemma 7 R->L }
% 0.20/0.41 divide(divide(divide(multiply(multiply(inverse(Y), X), multiply(inverse(Y), X)), multiply(inverse(Y), multiply(inverse(Y), X))), divide(multiply(inverse(Y), X), multiply(inverse(Y), multiply(inverse(Y), X)))), inverse(Y))
% 0.20/0.41 = { by lemma 3 }
% 0.20/0.41 divide(multiply(inverse(Y), X), inverse(Y))
% 0.20/0.41 = { by lemma 6 }
% 0.20/0.41 X
% 0.20/0.41
% 0.20/0.41 Lemma 9: multiply(Y, X) = multiply(X, Y).
% 0.20/0.41 Proof:
% 0.20/0.41 multiply(Y, X)
% 0.20/0.41 = { by lemma 6 R->L }
% 0.20/0.41 multiply(divide(multiply(X, Y), X), X)
% 0.20/0.41 = { by lemma 8 }
% 0.20/0.41 multiply(X, 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 9 R->L }
% 0.20/0.41 multiply(c3, multiply(a3, b3))
% 0.20/0.41 = { by lemma 9 }
% 0.20/0.41 multiply(c3, multiply(b3, a3))
% 0.20/0.41 = { by lemma 9 }
% 0.20/0.41 multiply(multiply(b3, a3), c3)
% 0.20/0.41 = { by lemma 8 R->L }
% 0.20/0.41 multiply(divide(multiply(multiply(b3, a3), c3), multiply(b3, c3)), multiply(b3, c3))
% 0.20/0.41 = { by lemma 7 }
% 0.20/0.41 multiply(a3, multiply(b3, c3))
% 0.20/0.41 % SZS output end Proof
% 0.20/0.41
% 0.20/0.41 RESULT: Unsatisfiable (the axioms are contradictory).
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