TSTP Solution File: BOO071-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : BOO071-1 : 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 : n005.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 : Wed Aug 30 18:11:36 EDT 2023
% Result : Unsatisfiable 0.21s 0.60s
% 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 : BOO071-1 : TPTP v8.1.2. Released v2.6.0.
% 0.07/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.14/0.34 % Computer : n005.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Aug 27 08:08:08 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.60 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.21/0.60
% 0.21/0.60 % SZS status Unsatisfiable
% 0.21/0.60
% 0.21/0.61 % SZS output start Proof
% 0.21/0.61 Axiom 1 (single_axiom): multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, V), U, multiply(Z, W, T))), multiply(W, multiply(T, U, V), Z)) = Y.
% 0.21/0.61
% 0.21/0.61 Lemma 2: multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, multiply(V, multiply(U, T, S), X2)), inverse(multiply(multiply(X2, V, S), T, multiply(X2, V, U))), multiply(Z, W, multiply(Y2, inverse(Y2), Z2)))), multiply(W, Z2, Z)) = Y.
% 0.21/0.61 Proof:
% 0.21/0.61 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, multiply(V, multiply(U, T, S), X2)), inverse(multiply(multiply(X2, V, S), T, multiply(X2, V, U))), multiply(Z, W, multiply(Y2, inverse(Y2), Z2)))), multiply(W, Z2, Z))
% 0.21/0.61 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.61 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, W, multiply(V, multiply(U, T, S), X2)), inverse(multiply(multiply(X2, V, S), T, multiply(X2, V, U))), multiply(Z, W, multiply(Y2, inverse(Y2), Z2)))), multiply(W, multiply(multiply(Y2, inverse(Y2), Z2), inverse(multiply(multiply(X2, V, S), T, multiply(X2, V, U))), multiply(V, multiply(U, T, S), X2)), Z))
% 0.21/0.61 = { by axiom 1 (single_axiom) }
% 0.21/0.61 Y
% 0.21/0.61
% 0.21/0.61 Lemma 3: multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, inverse(Z), multiply(W, inverse(W), V))), multiply(inverse(Z), V, Z)) = Y.
% 0.21/0.61 Proof:
% 0.21/0.61 multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, inverse(Z), multiply(W, inverse(W), V))), multiply(inverse(Z), V, Z))
% 0.21/0.61 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.61 multiply(multiply(X, inverse(X), Y), inverse(multiply(Z, multiply(multiply(U, inverse(U), inverse(Z)), inverse(multiply(multiply(T, S, X2), Y2, multiply(T, S, Z2))), multiply(S, multiply(Z2, Y2, X2), T)), multiply(W, inverse(W), V))), multiply(inverse(Z), V, Z))
% 0.21/0.61 = { by lemma 2 R->L }
% 0.21/0.61 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), multiply(Z, multiply(multiply(U, inverse(U), inverse(Z)), inverse(multiply(multiply(T, S, X2), Y2, multiply(T, S, Z2))), multiply(S, multiply(Z2, Y2, X2), T)), multiply(W, inverse(W), V))), inverse(multiply(multiply(multiply(W, inverse(W), V), Z, multiply(S, multiply(Z2, Y2, X2), T)), inverse(multiply(multiply(T, S, X2), Y2, multiply(T, S, Z2))), multiply(multiply(W, inverse(W), V), Z, multiply(U, inverse(U), inverse(Z))))), multiply(Z, inverse(Z), multiply(W, inverse(W), V)))), multiply(inverse(Z), V, Z))
% 0.21/0.61 = { by lemma 2 }
% 0.21/0.61 Y
% 0.21/0.61
% 0.21/0.61 Lemma 4: multiply(inverse(X), Y, X) = Y.
% 0.21/0.61 Proof:
% 0.21/0.61 multiply(inverse(X), Y, X)
% 0.21/0.61 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.61 multiply(multiply(multiply(X, inverse(X), multiply(Z, inverse(Z), Y)), inverse(multiply(X, inverse(X), multiply(Z, inverse(Z), Y))), multiply(inverse(X), Y, X)), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.61 = { by lemma 3 }
% 0.21/0.61 multiply(multiply(Z, inverse(Z), Y), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.61 = { by axiom 1 (single_axiom) }
% 0.21/0.61 Y
% 0.21/0.61
% 0.21/0.61 Lemma 5: multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V)) = multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z).
% 0.21/0.61 Proof:
% 0.21/0.61 multiply(multiply(Z, X, Y), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
% 0.21/0.61 = { by axiom 1 (single_axiom) R->L }
% 0.21/0.61 multiply(multiply(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y)), inverse(multiply(multiply(Z, X, W), inverse(multiply(Z, X, W)), multiply(Z, X, Y))), multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)), inverse(multiply(multiply(V, U, T), S, multiply(V, U, X2))), multiply(U, multiply(X2, S, T), V))
% 0.21/0.61 = { by axiom 1 (single_axiom) }
% 0.21/0.61 multiply(X, multiply(Y, inverse(multiply(Z, X, W)), W), Z)
% 0.21/0.61
% 0.21/0.61 Lemma 6: multiply(inverse(X), multiply(Y, inverse(multiply(X, inverse(X), Z)), Z), X) = Y.
% 0.21/0.61 Proof:
% 0.21/0.61 multiply(inverse(X), multiply(Y, inverse(multiply(X, inverse(X), Z)), Z), X)
% 0.21/0.61 = { by lemma 5 R->L }
% 0.21/0.61 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.61 = { by axiom 1 (single_axiom) }
% 0.21/0.61 Y
% 0.21/0.61
% 0.21/0.61 Lemma 7: inverse(multiply(X, inverse(X), Y)) = inverse(Y).
% 0.21/0.61 Proof:
% 0.21/0.61 inverse(multiply(X, inverse(X), Y))
% 0.21/0.61 = { by lemma 4 R->L }
% 0.21/0.61 multiply(inverse(X), inverse(multiply(X, inverse(X), Y)), X)
% 0.21/0.61 = { by lemma 4 R->L }
% 0.21/0.61 multiply(inverse(X), multiply(inverse(Y), inverse(multiply(X, inverse(X), Y)), Y), X)
% 0.21/0.61 = { by lemma 6 }
% 0.21/0.61 inverse(Y)
% 0.21/0.61
% 0.21/0.61 Lemma 8: multiply(X, inverse(Y), Y) = X.
% 0.21/0.61 Proof:
% 0.21/0.61 multiply(X, inverse(Y), Y)
% 0.21/0.61 = { by lemma 4 R->L }
% 0.21/0.61 multiply(inverse(Z), multiply(X, inverse(Y), Y), Z)
% 0.21/0.61 = { by lemma 7 R->L }
% 0.21/0.61 multiply(inverse(Z), multiply(X, inverse(multiply(Z, inverse(Z), Y)), Y), Z)
% 0.21/0.61 = { by lemma 5 R->L }
% 0.21/0.61 multiply(multiply(Z, inverse(Z), X), inverse(multiply(multiply(W, V, U), T, multiply(W, V, S))), multiply(V, multiply(S, T, U), W))
% 0.21/0.61 = { by axiom 1 (single_axiom) }
% 0.21/0.61 X
% 0.21/0.61
% 0.21/0.61 Lemma 9: multiply(X, inverse(X), Y) = Y.
% 0.21/0.61 Proof:
% 0.21/0.61 multiply(X, inverse(X), Y)
% 0.21/0.61 = { by lemma 8 R->L }
% 0.21/0.61 multiply(multiply(X, inverse(X), Y), inverse(Z), Z)
% 0.21/0.61 = { by lemma 7 R->L }
% 0.21/0.61 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), Z)), Z)
% 0.21/0.61 = { by lemma 8 R->L }
% 0.21/0.61 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), Z))), Z)
% 0.21/0.61 = { by lemma 6 R->L }
% 0.21/0.61 multiply(multiply(X, inverse(X), Y), inverse(multiply(multiply(Z, inverse(Z), W), inverse(multiply(Z, inverse(Z), W)), multiply(Z, inverse(Z), Z))), multiply(inverse(Z), multiply(Z, inverse(multiply(Z, inverse(Z), W)), W), Z))
% 0.21/0.61 = { by axiom 1 (single_axiom) }
% 0.21/0.61 Y
% 0.21/0.61
% 0.21/0.61 Goal 1 (prove_tba_axioms_5): multiply(inverse(b), b, a) = a.
% 0.21/0.61 Proof:
% 0.21/0.61 multiply(inverse(b), b, a)
% 0.21/0.61 = { by lemma 8 R->L }
% 0.21/0.61 multiply(multiply(inverse(b), b, a), inverse(X), X)
% 0.21/0.61 = { by lemma 4 R->L }
% 0.21/0.61 multiply(multiply(inverse(b), b, a), inverse(X), multiply(inverse(Y), X, Y))
% 0.21/0.61 = { by lemma 9 R->L }
% 0.21/0.61 multiply(multiply(inverse(b), b, a), inverse(multiply(Z, inverse(Z), X)), multiply(inverse(Y), X, Y))
% 0.21/0.61 = { by lemma 9 R->L }
% 0.21/0.61 multiply(multiply(inverse(b), b, a), inverse(multiply(Y, inverse(Y), multiply(Z, inverse(Z), X))), multiply(inverse(Y), X, Y))
% 0.21/0.61 = { by lemma 9 R->L }
% 0.21/0.61 multiply(multiply(inverse(b), multiply(inverse(b), inverse(inverse(b)), b), a), inverse(multiply(Y, inverse(Y), multiply(Z, inverse(Z), X))), multiply(inverse(Y), X, Y))
% 0.21/0.61 = { by lemma 4 }
% 0.21/0.61 multiply(multiply(inverse(b), inverse(inverse(b)), a), inverse(multiply(Y, inverse(Y), multiply(Z, inverse(Z), X))), multiply(inverse(Y), X, Y))
% 0.21/0.61 = { by lemma 3 }
% 0.21/0.61 a
% 0.21/0.61 % SZS output end Proof
% 0.21/0.61
% 0.21/0.61 RESULT: Unsatisfiable (the axioms are contradictory).
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