TSTP Solution File: GRP556-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP556-1 : 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 : n028.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 01:18:54 EDT 2023
% Result : Unsatisfiable 0.21s 0.39s
% Output : Proof 0.21s
% 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 : GRP556-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 : n028.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 02:34:55 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.39 Command-line arguments: --no-flatten-goal
% 0.21/0.39
% 0.21/0.39 % SZS status Unsatisfiable
% 0.21/0.39
% 0.21/0.40 % SZS output start Proof
% 0.21/0.40 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.21/0.40 Axiom 2 (single_axiom): divide(divide(X, inverse(divide(Y, divide(X, Z)))), Z) = Y.
% 0.21/0.40
% 0.21/0.40 Lemma 3: divide(multiply(X, divide(Y, divide(X, Z))), Z) = Y.
% 0.21/0.40 Proof:
% 0.21/0.40 divide(multiply(X, divide(Y, divide(X, Z))), Z)
% 0.21/0.40 = { by axiom 1 (multiply) }
% 0.21/0.40 divide(divide(X, inverse(divide(Y, divide(X, Z)))), Z)
% 0.21/0.40 = { by axiom 2 (single_axiom) }
% 0.21/0.40 Y
% 0.21/0.40
% 0.21/0.40 Lemma 4: multiply(X, divide(Y, divide(X, divide(Z, W)))) = divide(multiply(Z, Y), W).
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(X, divide(Y, divide(X, divide(Z, W))))
% 0.21/0.40 = { by lemma 3 R->L }
% 0.21/0.40 divide(multiply(Z, divide(multiply(X, divide(Y, divide(X, divide(Z, W)))), divide(Z, W))), W)
% 0.21/0.40 = { by lemma 3 }
% 0.21/0.40 divide(multiply(Z, Y), W)
% 0.21/0.40
% 0.21/0.40 Lemma 5: divide(multiply(multiply(X, Y), Z), multiply(X, Z)) = Y.
% 0.21/0.40 Proof:
% 0.21/0.40 divide(multiply(multiply(X, Y), Z), multiply(X, Z))
% 0.21/0.40 = { by axiom 1 (multiply) }
% 0.21/0.40 divide(multiply(multiply(X, Y), Z), divide(X, inverse(Z)))
% 0.21/0.40 = { by axiom 1 (multiply) }
% 0.21/0.40 divide(divide(multiply(X, Y), inverse(Z)), divide(X, inverse(Z)))
% 0.21/0.40 = { by lemma 4 R->L }
% 0.21/0.40 divide(multiply(W, divide(Y, divide(W, divide(X, inverse(Z))))), divide(X, inverse(Z)))
% 0.21/0.40 = { by lemma 3 }
% 0.21/0.40 Y
% 0.21/0.40
% 0.21/0.40 Lemma 6: multiply(X, divide(Y, Y)) = X.
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(X, divide(Y, Y))
% 0.21/0.40 = { by lemma 5 R->L }
% 0.21/0.40 multiply(divide(multiply(multiply(Z, X), Y), multiply(Z, Y)), divide(Y, Y))
% 0.21/0.40 = { by lemma 4 R->L }
% 0.21/0.40 multiply(multiply(W, divide(Y, divide(W, divide(multiply(Z, X), multiply(Z, Y))))), divide(Y, Y))
% 0.21/0.40 = { by lemma 3 R->L }
% 0.21/0.40 multiply(multiply(W, divide(Y, divide(W, divide(multiply(Z, X), multiply(Z, Y))))), divide(Y, divide(multiply(W, divide(Y, divide(W, divide(multiply(Z, X), multiply(Z, Y))))), divide(multiply(Z, X), multiply(Z, Y)))))
% 0.21/0.40 = { by lemma 4 }
% 0.21/0.40 divide(multiply(multiply(Z, X), Y), multiply(Z, Y))
% 0.21/0.40 = { by lemma 5 }
% 0.21/0.40 X
% 0.21/0.40
% 0.21/0.40 Lemma 7: multiply(X, divide(Y, X)) = Y.
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(X, divide(Y, X))
% 0.21/0.40 = { by lemma 6 R->L }
% 0.21/0.40 multiply(X, divide(Y, multiply(X, divide(Z, Z))))
% 0.21/0.40 = { by lemma 6 R->L }
% 0.21/0.40 multiply(multiply(X, divide(Y, multiply(X, divide(Z, Z)))), divide(Z, Z))
% 0.21/0.40 = { by axiom 1 (multiply) }
% 0.21/0.40 multiply(multiply(X, divide(Y, divide(X, inverse(divide(Z, Z))))), divide(Z, Z))
% 0.21/0.40 = { by axiom 1 (multiply) }
% 0.21/0.40 divide(multiply(X, divide(Y, divide(X, inverse(divide(Z, Z))))), inverse(divide(Z, Z)))
% 0.21/0.40 = { by lemma 3 }
% 0.21/0.40 Y
% 0.21/0.40
% 0.21/0.40 Lemma 8: multiply(divide(X, X), Y) = Y.
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(divide(X, X), Y)
% 0.21/0.40 = { by lemma 3 R->L }
% 0.21/0.40 multiply(divide(X, X), divide(multiply(X, divide(Y, divide(X, X))), X))
% 0.21/0.40 = { by lemma 6 R->L }
% 0.21/0.40 multiply(divide(X, X), divide(multiply(X, divide(Y, divide(X, X))), multiply(X, divide(Z, Z))))
% 0.21/0.40 = { by lemma 6 R->L }
% 0.21/0.40 multiply(divide(X, X), divide(multiply(multiply(X, divide(Y, divide(X, X))), divide(Z, Z)), multiply(X, divide(Z, Z))))
% 0.21/0.40 = { by lemma 5 }
% 0.21/0.40 multiply(divide(X, X), divide(Y, divide(X, X)))
% 0.21/0.40 = { by lemma 7 }
% 0.21/0.40 Y
% 0.21/0.40
% 0.21/0.40 Goal 1 (prove_these_axioms_4): multiply(a, b) = multiply(b, a).
% 0.21/0.40 Proof:
% 0.21/0.40 multiply(a, b)
% 0.21/0.40 = { by lemma 8 R->L }
% 0.21/0.40 multiply(multiply(divide(X, X), a), b)
% 0.21/0.40 = { by lemma 7 R->L }
% 0.21/0.40 multiply(multiply(divide(X, X), b), divide(multiply(multiply(divide(X, X), a), b), multiply(divide(X, X), b)))
% 0.21/0.40 = { by lemma 5 }
% 0.21/0.40 multiply(multiply(divide(X, X), b), a)
% 0.21/0.40 = { by lemma 8 }
% 0.21/0.40 multiply(b, a)
% 0.21/0.40 % SZS output end Proof
% 0.21/0.40
% 0.21/0.40 RESULT: Unsatisfiable (the axioms are contradictory).
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