TSTP Solution File: GRP564-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP564-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n025.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 01:18:56 EDT 2023
% Result : Unsatisfiable 0.19s 0.39s
% 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 : GRP564-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n025.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 : Tue Aug 29 02:52:55 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.39 Command-line arguments: --no-flatten-goal
% 0.19/0.39
% 0.19/0.39 % SZS status Unsatisfiable
% 0.19/0.39
% 0.19/0.40 % SZS output start Proof
% 0.19/0.40 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.19/0.40 Axiom 2 (single_axiom): divide(divide(divide(X, inverse(Y)), Z), divide(X, Z)) = Y.
% 0.19/0.40
% 0.19/0.40 Lemma 3: divide(divide(multiply(X, Y), Z), divide(X, Z)) = Y.
% 0.19/0.40 Proof:
% 0.19/0.40 divide(divide(multiply(X, Y), Z), divide(X, Z))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 divide(divide(divide(X, inverse(Y)), Z), divide(X, Z))
% 0.19/0.40 = { by axiom 2 (single_axiom) }
% 0.19/0.40 Y
% 0.19/0.40
% 0.19/0.40 Lemma 4: divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), Y) = W.
% 0.19/0.40 Proof:
% 0.19/0.40 divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), Y)
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), divide(divide(multiply(X, Y), Z), divide(X, Z)))
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 W
% 0.19/0.40
% 0.19/0.40 Lemma 5: multiply(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), Y) = W.
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), Y)
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 divide(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), inverse(Y))
% 0.19/0.40 = { by lemma 4 }
% 0.19/0.40 W
% 0.19/0.40
% 0.19/0.40 Lemma 6: divide(multiply(X, Y), X) = Y.
% 0.19/0.40 Proof:
% 0.19/0.40 divide(multiply(X, Y), X)
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 divide(divide(X, inverse(Y)), X)
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 divide(divide(X, divide(divide(multiply(Z, inverse(Y)), W), divide(Z, W))), X)
% 0.19/0.40 = { by lemma 5 R->L }
% 0.19/0.40 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)
% 0.19/0.40 = { by lemma 4 }
% 0.19/0.40 Y
% 0.19/0.40
% 0.19/0.40 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.19/0.40 Proof:
% 0.19/0.40 multiply(a, b)
% 0.19/0.40 = { by lemma 6 R->L }
% 0.19/0.40 multiply(divide(multiply(b, a), b), b)
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 divide(divide(multiply(b, a), b), inverse(b))
% 0.19/0.40 = { by lemma 6 R->L }
% 0.19/0.40 divide(divide(multiply(b, a), divide(multiply(multiply(inverse(b), multiply(inverse(b), multiply(b, a))), b), multiply(inverse(b), multiply(inverse(b), multiply(b, a))))), inverse(b))
% 0.19/0.40 = { by axiom 1 (multiply) }
% 0.19/0.40 divide(divide(multiply(b, a), divide(multiply(divide(inverse(b), inverse(multiply(inverse(b), multiply(b, a)))), b), multiply(inverse(b), multiply(inverse(b), multiply(b, a))))), inverse(b))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 divide(divide(multiply(b, a), divide(multiply(divide(inverse(b), divide(divide(multiply(X, inverse(multiply(inverse(b), multiply(b, a)))), Y), divide(X, Y))), b), multiply(inverse(b), multiply(inverse(b), multiply(b, a))))), inverse(b))
% 0.19/0.40 = { by lemma 5 R->L }
% 0.19/0.40 divide(divide(multiply(b, a), divide(multiply(divide(multiply(divide(multiply(divide(multiply(X, inverse(multiply(inverse(b), multiply(b, a)))), Y), inverse(b)), divide(X, Y)), multiply(inverse(b), multiply(b, a))), divide(divide(multiply(X, inverse(multiply(inverse(b), multiply(b, a)))), Y), divide(X, Y))), b), multiply(inverse(b), multiply(inverse(b), multiply(b, a))))), inverse(b))
% 0.19/0.40 = { by lemma 5 }
% 0.19/0.40 divide(divide(multiply(b, a), divide(multiply(inverse(b), multiply(b, a)), multiply(inverse(b), multiply(inverse(b), multiply(b, a))))), inverse(b))
% 0.19/0.40 = { by lemma 3 R->L }
% 0.19/0.40 divide(divide(divide(divide(multiply(inverse(b), multiply(b, a)), inverse(multiply(inverse(b), multiply(b, a)))), divide(inverse(b), inverse(multiply(inverse(b), multiply(b, a))))), divide(multiply(inverse(b), multiply(b, a)), multiply(inverse(b), multiply(inverse(b), multiply(b, a))))), inverse(b))
% 0.19/0.40 = { by axiom 1 (multiply) R->L }
% 0.19/0.40 divide(divide(divide(multiply(multiply(inverse(b), multiply(b, a)), multiply(inverse(b), multiply(b, a))), divide(inverse(b), inverse(multiply(inverse(b), multiply(b, a))))), divide(multiply(inverse(b), multiply(b, a)), multiply(inverse(b), multiply(inverse(b), multiply(b, a))))), inverse(b))
% 0.19/0.40 = { by axiom 1 (multiply) R->L }
% 0.19/0.40 divide(divide(divide(multiply(multiply(inverse(b), multiply(b, a)), multiply(inverse(b), multiply(b, a))), multiply(inverse(b), multiply(inverse(b), multiply(b, a)))), divide(multiply(inverse(b), multiply(b, a)), multiply(inverse(b), multiply(inverse(b), multiply(b, a))))), inverse(b))
% 0.19/0.40 = { by lemma 3 }
% 0.19/0.40 divide(multiply(inverse(b), multiply(b, a)), inverse(b))
% 0.19/0.40 = { by lemma 6 }
% 0.19/0.40 multiply(b, a)
% 0.19/0.40 % SZS output end Proof
% 0.19/0.40
% 0.19/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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