TSTP Solution File: GRP561-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP561-1 : 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 01:18:55 EDT 2023
% Result : Unsatisfiable 0.13s 0.37s
% Output : Proof 0.18s
% 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 : GRP561-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n007.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 00:47:43 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.13/0.37 Command-line arguments: --no-flatten-goal
% 0.13/0.37
% 0.13/0.37 % SZS status Unsatisfiable
% 0.13/0.37
% 0.18/0.38 % SZS output start Proof
% 0.18/0.38 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.18/0.38 Axiom 2 (single_axiom): divide(divide(divide(X, inverse(Y)), Z), divide(X, Z)) = Y.
% 0.18/0.38
% 0.18/0.38 Lemma 3: divide(divide(multiply(X, Y), Z), divide(X, Z)) = Y.
% 0.18/0.38 Proof:
% 0.18/0.38 divide(divide(multiply(X, Y), Z), divide(X, Z))
% 0.18/0.38 = { by axiom 1 (multiply) }
% 0.18/0.38 divide(divide(divide(X, inverse(Y)), Z), divide(X, Z))
% 0.18/0.38 = { by axiom 2 (single_axiom) }
% 0.18/0.38 Y
% 0.18/0.38
% 0.18/0.38 Lemma 4: divide(multiply(multiply(X, Y), Z), multiply(X, Z)) = Y.
% 0.18/0.38 Proof:
% 0.18/0.38 divide(multiply(multiply(X, Y), Z), multiply(X, Z))
% 0.18/0.38 = { by axiom 1 (multiply) }
% 0.18/0.38 divide(multiply(multiply(X, Y), Z), divide(X, inverse(Z)))
% 0.18/0.38 = { by axiom 1 (multiply) }
% 0.18/0.38 divide(divide(multiply(X, Y), inverse(Z)), divide(X, inverse(Z)))
% 0.18/0.38 = { by lemma 3 }
% 0.18/0.39 Y
% 0.18/0.39
% 0.18/0.39 Lemma 5: divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), Y) = W.
% 0.18/0.39 Proof:
% 0.18/0.39 divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), Y)
% 0.18/0.39 = { by lemma 3 R->L }
% 0.18/0.39 divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), divide(divide(multiply(X, Y), Z), divide(X, Z)))
% 0.18/0.39 = { by lemma 3 }
% 0.18/0.39 W
% 0.18/0.39
% 0.18/0.39 Lemma 6: multiply(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), Y) = W.
% 0.18/0.39 Proof:
% 0.18/0.39 multiply(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), Y)
% 0.18/0.39 = { by axiom 1 (multiply) }
% 0.18/0.39 divide(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), inverse(Y))
% 0.18/0.39 = { by lemma 5 }
% 0.18/0.39 W
% 0.18/0.39
% 0.18/0.39 Lemma 7: divide(multiply(X, Y), X) = Y.
% 0.18/0.39 Proof:
% 0.18/0.39 divide(multiply(X, Y), X)
% 0.18/0.39 = { by axiom 1 (multiply) }
% 0.18/0.39 divide(divide(X, inverse(Y)), X)
% 0.18/0.39 = { by lemma 3 R->L }
% 0.18/0.39 divide(divide(X, divide(divide(multiply(Z, inverse(Y)), W), divide(Z, W))), X)
% 0.18/0.39 = { by lemma 6 R->L }
% 0.18/0.39 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)
% 0.18/0.39 = { by lemma 5 }
% 0.18/0.39 Y
% 0.18/0.39
% 0.18/0.39 Lemma 8: multiply(inverse(X), Y) = divide(Y, X).
% 0.18/0.39 Proof:
% 0.18/0.39 multiply(inverse(X), Y)
% 0.18/0.39 = { by lemma 3 R->L }
% 0.18/0.39 divide(divide(multiply(multiply(inverse(X), Y), multiply(inverse(X), Y)), multiply(inverse(X), multiply(inverse(X), Y))), divide(multiply(inverse(X), Y), multiply(inverse(X), multiply(inverse(X), Y))))
% 0.18/0.39 = { by lemma 4 }
% 0.18/0.39 divide(Y, divide(multiply(inverse(X), Y), multiply(inverse(X), multiply(inverse(X), Y))))
% 0.18/0.39 = { by lemma 6 R->L }
% 0.18/0.39 divide(Y, divide(multiply(divide(multiply(divide(multiply(divide(multiply(Z, inverse(multiply(inverse(X), Y))), W), inverse(X)), divide(Z, W)), multiply(inverse(X), Y)), divide(divide(multiply(Z, inverse(multiply(inverse(X), Y))), W), divide(Z, W))), X), multiply(inverse(X), multiply(inverse(X), Y))))
% 0.18/0.39 = { by lemma 6 }
% 0.18/0.39 divide(Y, divide(multiply(divide(inverse(X), divide(divide(multiply(Z, inverse(multiply(inverse(X), Y))), W), divide(Z, W))), X), multiply(inverse(X), multiply(inverse(X), Y))))
% 0.18/0.39 = { by lemma 3 }
% 0.18/0.39 divide(Y, divide(multiply(divide(inverse(X), inverse(multiply(inverse(X), Y))), X), multiply(inverse(X), multiply(inverse(X), Y))))
% 0.18/0.39 = { by axiom 1 (multiply) R->L }
% 0.18/0.39 divide(Y, divide(multiply(multiply(inverse(X), multiply(inverse(X), Y)), X), multiply(inverse(X), multiply(inverse(X), Y))))
% 0.18/0.39 = { by lemma 7 }
% 0.18/0.39 divide(Y, X)
% 0.18/0.39
% 0.18/0.39 Lemma 9: multiply(divide(X, X), Y) = Y.
% 0.18/0.39 Proof:
% 0.18/0.39 multiply(divide(X, X), Y)
% 0.18/0.39 = { by lemma 3 R->L }
% 0.18/0.39 divide(divide(multiply(X, multiply(divide(X, X), Y)), X), divide(X, X))
% 0.18/0.39 = { by lemma 7 }
% 0.18/0.39 divide(multiply(divide(X, X), Y), divide(X, X))
% 0.18/0.39 = { by lemma 7 }
% 0.18/0.39 Y
% 0.18/0.39
% 0.18/0.39 Goal 1 (prove_these_axioms_1): multiply(inverse(a1), a1) = multiply(inverse(b1), b1).
% 0.18/0.39 Proof:
% 0.18/0.39 multiply(inverse(a1), a1)
% 0.18/0.39 = { by lemma 8 }
% 0.18/0.39 divide(a1, a1)
% 0.18/0.39 = { by lemma 9 R->L }
% 0.18/0.39 divide(multiply(divide(b1, b1), a1), a1)
% 0.18/0.39 = { by lemma 9 R->L }
% 0.18/0.39 divide(multiply(divide(b1, b1), a1), multiply(divide(X, X), a1))
% 0.18/0.39 = { by lemma 9 R->L }
% 0.18/0.39 divide(multiply(multiply(divide(X, X), divide(b1, b1)), a1), multiply(divide(X, X), a1))
% 0.18/0.39 = { by lemma 4 }
% 0.18/0.39 divide(b1, b1)
% 0.18/0.39 = { by lemma 8 R->L }
% 0.18/0.39 multiply(inverse(b1), b1)
% 0.18/0.39 % SZS output end Proof
% 0.18/0.39
% 0.18/0.39 RESULT: Unsatisfiable (the axioms are contradictory).
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