TSTP Solution File: BOO034-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : BOO034-1 : TPTP v8.1.2. Released v2.2.0.
% 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 : Wed Aug 30 18:11:30 EDT 2023
% Result : Unsatisfiable 0.21s 0.40s
% 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
% 0.00/0.13 % Problem : BOO034-1 : TPTP v8.1.2. Released v2.2.0.
% 0.13/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.35 % Computer : n028.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sun Aug 27 08:22:53 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.40 Command-line arguments: --no-flatten-goal
% 0.21/0.40
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40
% 0.21/0.41 % SZS output start Proof
% 0.21/0.41 Axiom 1 (ternary_multiply_2): multiply(X, X, Y) = X.
% 0.21/0.41 Axiom 2 (ternary_multiply_1): multiply(X, Y, Y) = Y.
% 0.21/0.41 Axiom 3 (right_inverse): multiply(X, Y, inverse(Y)) = X.
% 0.21/0.41 Axiom 4 (associativity): multiply(multiply(X, Y, Z), W, multiply(X, Y, V)) = multiply(X, Y, multiply(Z, W, V)).
% 0.21/0.41
% 0.21/0.41 Lemma 5: multiply(X, Y, multiply(inverse(Y), Z, Y)) = multiply(X, Z, Y).
% 0.21/0.41 Proof:
% 0.21/0.41 multiply(X, Y, multiply(inverse(Y), Z, Y))
% 0.21/0.41 = { by axiom 4 (associativity) R->L }
% 0.21/0.41 multiply(multiply(X, Y, inverse(Y)), Z, multiply(X, Y, Y))
% 0.21/0.41 = { by axiom 2 (ternary_multiply_1) }
% 0.21/0.41 multiply(multiply(X, Y, inverse(Y)), Z, Y)
% 0.21/0.41 = { by axiom 3 (right_inverse) }
% 0.21/0.41 multiply(X, Z, Y)
% 0.21/0.41
% 0.21/0.41 Lemma 6: multiply(Y, Z, multiply(X, Y, W)) = multiply(X, Y, multiply(Y, Z, W)).
% 0.21/0.41 Proof:
% 0.21/0.41 multiply(Y, Z, multiply(X, Y, W))
% 0.21/0.42 = { by axiom 2 (ternary_multiply_1) R->L }
% 0.21/0.42 multiply(multiply(X, Y, Y), Z, multiply(X, Y, W))
% 0.21/0.42 = { by axiom 4 (associativity) }
% 0.21/0.42 multiply(X, Y, multiply(Y, Z, W))
% 0.21/0.42
% 0.21/0.42 Lemma 7: multiply(X, Y, Z) = multiply(X, Z, Y).
% 0.21/0.42 Proof:
% 0.21/0.42 multiply(X, Y, Z)
% 0.21/0.42 = { by lemma 5 R->L }
% 0.21/0.42 multiply(X, Z, multiply(inverse(Z), Y, Z))
% 0.21/0.42 = { by axiom 2 (ternary_multiply_1) R->L }
% 0.21/0.42 multiply(X, Z, multiply(inverse(Z), Y, multiply(Y, Z, Z)))
% 0.21/0.42 = { by lemma 6 R->L }
% 0.21/0.42 multiply(X, Z, multiply(Y, Z, multiply(inverse(Z), Y, Z)))
% 0.21/0.42 = { by lemma 5 }
% 0.21/0.42 multiply(X, Z, multiply(Y, Y, Z))
% 0.21/0.42 = { by axiom 1 (ternary_multiply_2) }
% 0.21/0.42 multiply(X, Z, Y)
% 0.21/0.42
% 0.21/0.42 Lemma 8: multiply(X, inverse(X), Y) = Y.
% 0.21/0.42 Proof:
% 0.21/0.42 multiply(X, inverse(X), Y)
% 0.21/0.42 = { by axiom 3 (right_inverse) R->L }
% 0.21/0.42 multiply(X, inverse(X), multiply(Y, X, inverse(X)))
% 0.21/0.42 = { by lemma 6 }
% 0.21/0.42 multiply(Y, X, multiply(X, inverse(X), inverse(X)))
% 0.21/0.42 = { by axiom 2 (ternary_multiply_1) }
% 0.21/0.42 multiply(Y, X, inverse(X))
% 0.21/0.42 = { by axiom 3 (right_inverse) }
% 0.21/0.42 Y
% 0.21/0.42
% 0.21/0.42 Lemma 9: multiply(Y, Z, X) = multiply(X, Y, Z).
% 0.21/0.42 Proof:
% 0.21/0.42 multiply(Y, Z, X)
% 0.21/0.42 = { by lemma 7 R->L }
% 0.21/0.42 multiply(Y, X, Z)
% 0.21/0.42 = { by lemma 8 R->L }
% 0.21/0.42 multiply(Y, X, multiply(X, inverse(X), Z))
% 0.21/0.42 = { by lemma 7 R->L }
% 0.21/0.42 multiply(Y, X, multiply(X, Z, inverse(X)))
% 0.21/0.42 = { by lemma 6 R->L }
% 0.21/0.42 multiply(X, Z, multiply(Y, X, inverse(X)))
% 0.21/0.42 = { by axiom 3 (right_inverse) }
% 0.21/0.42 multiply(X, Z, Y)
% 0.21/0.42 = { by lemma 7 }
% 0.21/0.42 multiply(X, Y, Z)
% 0.21/0.42
% 0.21/0.42 Goal 1 (prove_single_axiom): multiply(multiply(a, inverse(a), b), inverse(multiply(multiply(c, d, e), f, multiply(c, d, g))), multiply(d, multiply(g, f, e), c)) = b.
% 0.21/0.42 Proof:
% 0.21/0.42 multiply(multiply(a, inverse(a), b), inverse(multiply(multiply(c, d, e), f, multiply(c, d, g))), multiply(d, multiply(g, f, e), c))
% 0.21/0.42 = { by axiom 4 (associativity) }
% 0.21/0.42 multiply(multiply(a, inverse(a), b), inverse(multiply(c, d, multiply(e, f, g))), multiply(d, multiply(g, f, e), c))
% 0.21/0.42 = { by lemma 8 }
% 0.21/0.42 multiply(b, inverse(multiply(c, d, multiply(e, f, g))), multiply(d, multiply(g, f, e), c))
% 0.21/0.42 = { by lemma 7 }
% 0.21/0.42 multiply(b, multiply(d, multiply(g, f, e), c), inverse(multiply(c, d, multiply(e, f, g))))
% 0.21/0.42 = { by lemma 7 }
% 0.21/0.42 multiply(b, multiply(d, c, multiply(g, f, e)), inverse(multiply(c, d, multiply(e, f, g))))
% 0.21/0.42 = { by lemma 7 }
% 0.21/0.42 multiply(b, multiply(d, c, multiply(g, e, f)), inverse(multiply(c, d, multiply(e, f, g))))
% 0.21/0.42 = { by lemma 9 R->L }
% 0.21/0.42 multiply(b, multiply(c, multiply(g, e, f), d), inverse(multiply(c, d, multiply(e, f, g))))
% 0.21/0.42 = { by lemma 7 }
% 0.21/0.42 multiply(b, multiply(c, d, multiply(g, e, f)), inverse(multiply(c, d, multiply(e, f, g))))
% 0.21/0.42 = { by lemma 9 R->L }
% 0.21/0.42 multiply(b, multiply(c, d, multiply(e, f, g)), inverse(multiply(c, d, multiply(e, f, g))))
% 0.21/0.42 = { by axiom 3 (right_inverse) }
% 0.21/0.42 b
% 0.21/0.42 % SZS output end Proof
% 0.21/0.42
% 0.21/0.42 RESULT: Unsatisfiable (the axioms are contradictory).
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