TSTP Solution File: GRP205-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP205-1 : TPTP v8.1.2. Released v2.3.0.
% 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 : n021.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 01:17:46 EDT 2023
% Result : Unsatisfiable 0.18s 0.61s
% Output : Proof 1.69s
% 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 : GRP205-1 : TPTP v8.1.2. Released v2.3.0.
% 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 : n021.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 00:27:43 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.18/0.61 Command-line arguments: --ground-connectedness --complete-subsets
% 0.18/0.61
% 0.18/0.61 % SZS status Unsatisfiable
% 0.18/0.61
% 0.18/0.62 % SZS output start Proof
% 0.18/0.62 Axiom 1 (right_identity): multiply(X, identity) = X.
% 0.18/0.62 Axiom 2 (left_identity): multiply(identity, X) = X.
% 0.18/0.62 Axiom 3 (right_inverse): multiply(X, right_inverse(X)) = identity.
% 0.18/0.62 Axiom 4 (left_inverse): multiply(left_inverse(X), X) = identity.
% 0.18/0.62 Axiom 5 (left_division_multiply): left_division(X, multiply(X, Y)) = Y.
% 0.18/0.62 Axiom 6 (right_division_multiply): right_division(multiply(X, Y), Y) = X.
% 0.18/0.62 Axiom 7 (multiply_left_division): multiply(X, left_division(X, Y)) = Y.
% 1.69/0.62 Axiom 8 (multiply_right_division): multiply(right_division(X, Y), Y) = X.
% 1.69/0.62 Axiom 9 (moufang3): multiply(multiply(multiply(X, Y), X), Z) = multiply(X, multiply(Y, multiply(X, Z))).
% 1.69/0.62
% 1.69/0.62 Lemma 10: multiply(right_inverse(X), multiply(X, Y)) = Y.
% 1.69/0.62 Proof:
% 1.69/0.62 multiply(right_inverse(X), multiply(X, Y))
% 1.69/0.62 = { by axiom 5 (left_division_multiply) R->L }
% 1.69/0.62 left_division(X, multiply(X, multiply(right_inverse(X), multiply(X, Y))))
% 1.69/0.62 = { by axiom 9 (moufang3) R->L }
% 1.69/0.62 left_division(X, multiply(multiply(multiply(X, right_inverse(X)), X), Y))
% 1.69/0.62 = { by axiom 3 (right_inverse) }
% 1.69/0.62 left_division(X, multiply(multiply(identity, X), Y))
% 1.69/0.62 = { by axiom 2 (left_identity) }
% 1.69/0.62 left_division(X, multiply(X, Y))
% 1.69/0.62 = { by axiom 5 (left_division_multiply) }
% 1.69/0.62 Y
% 1.69/0.62
% 1.69/0.62 Lemma 11: left_division(right_inverse(X), Y) = multiply(X, Y).
% 1.69/0.62 Proof:
% 1.69/0.62 left_division(right_inverse(X), Y)
% 1.69/0.62 = { by lemma 10 R->L }
% 1.69/0.62 left_division(right_inverse(X), multiply(right_inverse(X), multiply(X, Y)))
% 1.69/0.62 = { by axiom 5 (left_division_multiply) }
% 1.69/0.62 multiply(X, Y)
% 1.69/0.62
% 1.69/0.62 Lemma 12: multiply(multiply(X, Y), X) = multiply(X, multiply(Y, X)).
% 1.69/0.62 Proof:
% 1.69/0.62 multiply(multiply(X, Y), X)
% 1.69/0.62 = { by axiom 1 (right_identity) R->L }
% 1.69/0.62 multiply(multiply(multiply(X, Y), X), identity)
% 1.69/0.62 = { by axiom 9 (moufang3) }
% 1.69/0.62 multiply(X, multiply(Y, multiply(X, identity)))
% 1.69/0.62 = { by axiom 1 (right_identity) }
% 1.69/0.62 multiply(X, multiply(Y, X))
% 1.69/0.62
% 1.69/0.62 Lemma 13: multiply(X, multiply(left_division(X, Y), X)) = multiply(Y, X).
% 1.69/0.62 Proof:
% 1.69/0.62 multiply(X, multiply(left_division(X, Y), X))
% 1.69/0.62 = { by lemma 12 R->L }
% 1.69/0.62 multiply(multiply(X, left_division(X, Y)), X)
% 1.69/0.62 = { by axiom 7 (multiply_left_division) }
% 1.69/0.62 multiply(Y, X)
% 1.69/0.62
% 1.69/0.62 Lemma 14: right_division(X, right_inverse(Y)) = multiply(X, Y).
% 1.69/0.62 Proof:
% 1.69/0.62 right_division(X, right_inverse(Y))
% 1.69/0.62 = { by axiom 7 (multiply_left_division) R->L }
% 1.69/0.62 right_division(multiply(Y, left_division(Y, X)), right_inverse(Y))
% 1.69/0.62 = { by axiom 1 (right_identity) R->L }
% 1.69/0.62 right_division(multiply(Y, multiply(left_division(Y, X), identity)), right_inverse(Y))
% 1.69/0.62 = { by axiom 3 (right_inverse) R->L }
% 1.69/0.62 right_division(multiply(Y, multiply(left_division(Y, X), multiply(Y, right_inverse(Y)))), right_inverse(Y))
% 1.69/0.62 = { by axiom 9 (moufang3) R->L }
% 1.69/0.62 right_division(multiply(multiply(multiply(Y, left_division(Y, X)), Y), right_inverse(Y)), right_inverse(Y))
% 1.69/0.62 = { by axiom 6 (right_division_multiply) }
% 1.69/0.62 multiply(multiply(Y, left_division(Y, X)), Y)
% 1.69/0.62 = { by lemma 12 }
% 1.69/0.62 multiply(Y, multiply(left_division(Y, X), Y))
% 1.69/0.62 = { by lemma 13 }
% 1.69/0.62 multiply(X, Y)
% 1.69/0.62
% 1.69/0.62 Lemma 15: multiply(multiply(X, multiply(Y, X)), Z) = multiply(X, multiply(Y, multiply(X, Z))).
% 1.69/0.62 Proof:
% 1.69/0.62 multiply(multiply(X, multiply(Y, X)), Z)
% 1.69/0.62 = { by lemma 12 R->L }
% 1.69/0.62 multiply(multiply(multiply(X, Y), X), Z)
% 1.69/0.62 = { by axiom 9 (moufang3) }
% 1.69/0.62 multiply(X, multiply(Y, multiply(X, Z)))
% 1.69/0.62
% 1.69/0.62 Goal 1 (prove_moufang4): multiply(x, multiply(multiply(y, z), x)) = multiply(multiply(x, y), multiply(z, x)).
% 1.69/0.62 Proof:
% 1.69/0.62 multiply(x, multiply(multiply(y, z), x))
% 1.69/0.62 = { by axiom 8 (multiply_right_division) R->L }
% 1.69/0.62 multiply(right_division(multiply(x, multiply(multiply(y, z), x)), multiply(z, x)), multiply(z, x))
% 1.69/0.62 = { by axiom 5 (left_division_multiply) R->L }
% 1.69/0.62 multiply(right_division(multiply(x, multiply(multiply(y, z), x)), left_division(left_inverse(multiply(z, x)), multiply(left_inverse(multiply(z, x)), multiply(z, x)))), multiply(z, x))
% 1.69/0.62 = { by axiom 4 (left_inverse) }
% 1.69/0.62 multiply(right_division(multiply(x, multiply(multiply(y, z), x)), left_division(left_inverse(multiply(z, x)), identity)), multiply(z, x))
% 1.69/0.62 = { by axiom 3 (right_inverse) R->L }
% 1.69/0.62 multiply(right_division(multiply(x, multiply(multiply(y, z), x)), left_division(left_inverse(multiply(z, x)), multiply(left_inverse(multiply(z, x)), right_inverse(left_inverse(multiply(z, x)))))), multiply(z, x))
% 1.69/0.62 = { by axiom 5 (left_division_multiply) }
% 1.69/0.62 multiply(right_division(multiply(x, multiply(multiply(y, z), x)), right_inverse(left_inverse(multiply(z, x)))), multiply(z, x))
% 1.69/0.62 = { by lemma 14 }
% 1.69/0.62 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), left_inverse(multiply(z, x))), multiply(z, x))
% 1.69/0.62 = { by axiom 6 (right_division_multiply) R->L }
% 1.69/0.62 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), right_division(multiply(left_inverse(multiply(z, x)), multiply(z, x)), multiply(z, x))), multiply(z, x))
% 1.69/0.62 = { by axiom 4 (left_inverse) }
% 1.69/0.62 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), right_division(identity, multiply(z, x))), multiply(z, x))
% 1.69/0.62 = { by axiom 5 (left_division_multiply) R->L }
% 1.69/0.62 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), right_division(left_division(multiply(z, x), multiply(multiply(z, x), identity)), multiply(z, x))), multiply(z, x))
% 1.69/0.63 = { by axiom 1 (right_identity) }
% 1.69/0.63 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), right_division(left_division(multiply(z, x), multiply(z, x)), multiply(z, x))), multiply(z, x))
% 1.69/0.63 = { by axiom 2 (left_identity) R->L }
% 1.69/0.63 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), right_division(left_division(multiply(z, x), multiply(identity, multiply(z, x))), multiply(z, x))), multiply(z, x))
% 1.69/0.63 = { by axiom 3 (right_inverse) R->L }
% 1.69/0.63 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), right_division(left_division(multiply(z, x), multiply(multiply(multiply(z, x), right_inverse(multiply(z, x))), multiply(z, x))), multiply(z, x))), multiply(z, x))
% 1.69/0.63 = { by lemma 12 }
% 1.69/0.63 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), right_division(left_division(multiply(z, x), multiply(multiply(z, x), multiply(right_inverse(multiply(z, x)), multiply(z, x)))), multiply(z, x))), multiply(z, x))
% 1.69/0.63 = { by axiom 5 (left_division_multiply) }
% 1.69/0.63 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), right_division(multiply(right_inverse(multiply(z, x)), multiply(z, x)), multiply(z, x))), multiply(z, x))
% 1.69/0.63 = { by axiom 6 (right_division_multiply) }
% 1.69/0.63 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), right_inverse(multiply(z, x))), multiply(z, x))
% 1.69/0.63 = { by axiom 5 (left_division_multiply) R->L }
% 1.69/0.63 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), left_division(right_division(right_inverse(z), right_inverse(multiply(z, x))), multiply(right_division(right_inverse(z), right_inverse(multiply(z, x))), right_inverse(multiply(z, x))))), multiply(z, x))
% 1.69/0.63 = { by axiom 8 (multiply_right_division) }
% 1.69/0.63 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), left_division(right_division(right_inverse(z), right_inverse(multiply(z, x))), right_inverse(z))), multiply(z, x))
% 1.69/0.63 = { by lemma 14 }
% 1.69/0.63 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), left_division(multiply(right_inverse(z), multiply(z, x)), right_inverse(z))), multiply(z, x))
% 1.69/0.63 = { by lemma 10 }
% 1.69/0.63 multiply(multiply(multiply(x, multiply(multiply(y, z), x)), left_division(x, right_inverse(z))), multiply(z, x))
% 1.69/0.63 = { by lemma 15 }
% 1.69/0.63 multiply(multiply(x, multiply(multiply(y, z), multiply(x, left_division(x, right_inverse(z))))), multiply(z, x))
% 1.69/0.63 = { by axiom 7 (multiply_left_division) }
% 1.69/0.63 multiply(multiply(x, multiply(multiply(y, z), right_inverse(z))), multiply(z, x))
% 1.69/0.63 = { by axiom 5 (left_division_multiply) R->L }
% 1.69/0.63 multiply(multiply(x, left_division(z, multiply(z, multiply(multiply(y, z), right_inverse(z))))), multiply(z, x))
% 1.69/0.63 = { by lemma 11 R->L }
% 1.69/0.63 multiply(multiply(x, left_division(z, left_division(right_inverse(z), multiply(multiply(y, z), right_inverse(z))))), multiply(z, x))
% 1.69/0.63 = { by lemma 13 R->L }
% 1.69/0.63 multiply(multiply(x, left_division(z, left_division(right_inverse(z), multiply(right_inverse(z), multiply(left_division(right_inverse(z), multiply(y, z)), right_inverse(z)))))), multiply(z, x))
% 1.69/0.63 = { by axiom 5 (left_division_multiply) }
% 1.69/0.63 multiply(multiply(x, left_division(z, multiply(left_division(right_inverse(z), multiply(y, z)), right_inverse(z)))), multiply(z, x))
% 1.69/0.63 = { by lemma 11 }
% 1.69/0.63 multiply(multiply(x, left_division(z, multiply(multiply(z, multiply(y, z)), right_inverse(z)))), multiply(z, x))
% 1.69/0.63 = { by lemma 15 }
% 1.69/0.63 multiply(multiply(x, left_division(z, multiply(z, multiply(y, multiply(z, right_inverse(z)))))), multiply(z, x))
% 1.69/0.63 = { by axiom 3 (right_inverse) }
% 1.69/0.63 multiply(multiply(x, left_division(z, multiply(z, multiply(y, identity)))), multiply(z, x))
% 1.69/0.63 = { by axiom 1 (right_identity) }
% 1.69/0.63 multiply(multiply(x, left_division(z, multiply(z, y))), multiply(z, x))
% 1.69/0.63 = { by axiom 5 (left_division_multiply) }
% 1.69/0.63 multiply(multiply(x, y), multiply(z, x))
% 1.69/0.63 % SZS output end Proof
% 1.69/0.63
% 1.69/0.63 RESULT: Unsatisfiable (the axioms are contradictory).
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