TSTP Solution File: GRP562-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP562-1 : 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 : n032.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 0.11s 0.33s
% Output : Proof 0.11s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : GRP562-1 : TPTP v8.1.2. Released v2.6.0.
% 0.08/0.10 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.11/0.30 % Computer : n032.cluster.edu
% 0.11/0.30 % Model : x86_64 x86_64
% 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.30 % Memory : 8042.1875MB
% 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.30 % CPULimit : 300
% 0.11/0.30 % WCLimit : 300
% 0.11/0.30 % DateTime : Mon Aug 28 20:50:31 EDT 2023
% 0.11/0.30 % CPUTime :
% 0.11/0.33 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.11/0.33
% 0.11/0.33 % SZS status Unsatisfiable
% 0.11/0.33
% 0.11/0.33 % SZS output start Proof
% 0.11/0.33 Axiom 1 (multiply): multiply(X, Y) = divide(X, inverse(Y)).
% 0.11/0.33 Axiom 2 (single_axiom): divide(divide(divide(X, inverse(Y)), Z), divide(X, Z)) = Y.
% 0.11/0.33
% 0.11/0.33 Lemma 3: divide(divide(multiply(X, Y), Z), divide(X, Z)) = Y.
% 0.11/0.33 Proof:
% 0.11/0.33 divide(divide(multiply(X, Y), Z), divide(X, Z))
% 0.11/0.33 = { by axiom 1 (multiply) }
% 0.11/0.33 divide(divide(divide(X, inverse(Y)), Z), divide(X, Z))
% 0.11/0.33 = { by axiom 2 (single_axiom) }
% 0.11/0.33 Y
% 0.11/0.33
% 0.11/0.33 Lemma 4: divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), Y) = W.
% 0.11/0.33 Proof:
% 0.11/0.33 divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), Y)
% 0.11/0.33 = { by lemma 3 R->L }
% 0.11/0.33 divide(divide(multiply(divide(multiply(X, Y), Z), W), divide(X, Z)), divide(divide(multiply(X, Y), Z), divide(X, Z)))
% 0.11/0.33 = { by lemma 3 }
% 0.11/0.33 W
% 0.11/0.33
% 0.11/0.33 Lemma 5: multiply(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), Y) = W.
% 0.11/0.33 Proof:
% 0.11/0.33 multiply(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), Y)
% 0.11/0.33 = { by axiom 1 (multiply) }
% 0.11/0.34 divide(divide(multiply(divide(multiply(X, inverse(Y)), Z), W), divide(X, Z)), inverse(Y))
% 0.11/0.34 = { by lemma 4 }
% 0.11/0.34 W
% 0.11/0.34
% 0.11/0.34 Goal 1 (prove_these_axioms_2): multiply(multiply(inverse(b2), b2), a2) = a2.
% 0.11/0.34 Proof:
% 0.11/0.34 multiply(multiply(inverse(b2), b2), a2)
% 0.11/0.34 = { by lemma 3 R->L }
% 0.11/0.34 divide(divide(multiply(inverse(b2), multiply(multiply(inverse(b2), b2), a2)), inverse(b2)), divide(inverse(b2), inverse(b2)))
% 0.11/0.34 = { by axiom 1 (multiply) R->L }
% 0.11/0.34 divide(multiply(multiply(inverse(b2), multiply(multiply(inverse(b2), b2), a2)), b2), divide(inverse(b2), inverse(b2)))
% 0.11/0.34 = { by axiom 1 (multiply) R->L }
% 0.11/0.34 divide(multiply(multiply(inverse(b2), multiply(multiply(inverse(b2), b2), a2)), b2), multiply(inverse(b2), b2))
% 0.11/0.34 = { by axiom 1 (multiply) }
% 0.11/0.34 divide(multiply(divide(inverse(b2), inverse(multiply(multiply(inverse(b2), b2), a2))), b2), multiply(inverse(b2), b2))
% 0.11/0.34 = { by lemma 3 R->L }
% 0.11/0.34 divide(multiply(divide(inverse(b2), divide(divide(multiply(X, inverse(multiply(multiply(inverse(b2), b2), a2))), Y), divide(X, Y))), b2), multiply(inverse(b2), b2))
% 0.11/0.34 = { by lemma 5 R->L }
% 0.11/0.34 divide(multiply(divide(multiply(divide(multiply(divide(multiply(X, inverse(multiply(multiply(inverse(b2), b2), a2))), Y), inverse(b2)), divide(X, Y)), multiply(multiply(inverse(b2), b2), a2)), divide(divide(multiply(X, inverse(multiply(multiply(inverse(b2), b2), a2))), Y), divide(X, Y))), b2), multiply(inverse(b2), b2))
% 0.11/0.34 = { by lemma 5 }
% 0.11/0.34 divide(multiply(multiply(inverse(b2), b2), a2), multiply(inverse(b2), b2))
% 0.11/0.34 = { by axiom 1 (multiply) }
% 0.11/0.34 divide(divide(multiply(inverse(b2), b2), inverse(a2)), multiply(inverse(b2), b2))
% 0.11/0.34 = { by lemma 3 R->L }
% 0.11/0.34 divide(divide(multiply(inverse(b2), b2), divide(divide(multiply(Z, inverse(a2)), W), divide(Z, W))), multiply(inverse(b2), b2))
% 0.11/0.34 = { by lemma 5 R->L }
% 0.11/0.34 divide(divide(multiply(divide(multiply(divide(multiply(Z, inverse(a2)), W), multiply(inverse(b2), b2)), divide(Z, W)), a2), divide(divide(multiply(Z, inverse(a2)), W), divide(Z, W))), multiply(inverse(b2), b2))
% 0.11/0.34 = { by lemma 4 }
% 0.11/0.34 a2
% 0.11/0.34 % SZS output end Proof
% 0.11/0.34
% 0.11/0.34 RESULT: Unsatisfiable (the axioms are contradictory).
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