TSTP Solution File: GRP200-1 by Twee---2.4.2
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%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : GRP200-1 : 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 : n025.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 01:17:45 EDT 2023
% Result : Unsatisfiable 0.19s 0.53s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP200-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue Aug 29 01:23:39 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.53 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.53
% 0.19/0.53 % SZS status Unsatisfiable
% 0.19/0.53
% 0.19/0.54 % SZS output start Proof
% 0.19/0.54 Axiom 1 (right_identity): multiply(X, identity) = X.
% 0.19/0.54 Axiom 2 (left_identity): multiply(identity, X) = X.
% 0.19/0.54 Axiom 3 (right_inverse): multiply(X, right_inverse(X)) = identity.
% 0.19/0.54 Axiom 4 (left_inverse): multiply(left_inverse(X), X) = identity.
% 0.19/0.54 Axiom 5 (multiply_left_division): multiply(X, left_division(X, Y)) = Y.
% 0.19/0.54 Axiom 6 (multiply_right_division): multiply(right_division(X, Y), Y) = X.
% 0.19/0.54 Axiom 7 (left_division_multiply): left_division(X, multiply(X, Y)) = Y.
% 0.19/0.54 Axiom 8 (right_division_multiply): right_division(multiply(X, Y), Y) = X.
% 0.19/0.54 Axiom 9 (moufang1): multiply(multiply(X, multiply(Y, Z)), X) = multiply(multiply(X, Y), multiply(Z, X)).
% 0.19/0.54
% 0.19/0.54 Lemma 10: multiply(multiply(X, Y), X) = multiply(X, multiply(Y, X)).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(multiply(X, Y), X)
% 0.19/0.54 = { by axiom 2 (left_identity) R->L }
% 0.19/0.54 multiply(multiply(X, multiply(identity, Y)), X)
% 0.19/0.54 = { by axiom 9 (moufang1) }
% 0.19/0.54 multiply(multiply(X, identity), multiply(Y, X))
% 0.19/0.54 = { by axiom 1 (right_identity) }
% 0.19/0.54 multiply(X, multiply(Y, X))
% 0.19/0.54
% 0.19/0.54 Lemma 11: left_division(X, identity) = right_inverse(X).
% 0.19/0.54 Proof:
% 0.19/0.54 left_division(X, identity)
% 0.19/0.54 = { by axiom 3 (right_inverse) R->L }
% 0.19/0.54 left_division(X, multiply(X, right_inverse(X)))
% 0.19/0.54 = { by axiom 7 (left_division_multiply) }
% 0.19/0.54 right_inverse(X)
% 0.19/0.54
% 0.19/0.54 Lemma 12: left_inverse(X) = right_inverse(X).
% 0.19/0.54 Proof:
% 0.19/0.54 left_inverse(X)
% 0.19/0.54 = { by axiom 7 (left_division_multiply) R->L }
% 0.19/0.54 left_division(X, multiply(X, left_inverse(X)))
% 0.19/0.54 = { by axiom 7 (left_division_multiply) R->L }
% 0.19/0.54 left_division(X, left_division(left_inverse(X), multiply(left_inverse(X), multiply(X, left_inverse(X)))))
% 0.19/0.54 = { by lemma 10 R->L }
% 0.19/0.54 left_division(X, left_division(left_inverse(X), multiply(multiply(left_inverse(X), X), left_inverse(X))))
% 0.19/0.54 = { by axiom 4 (left_inverse) }
% 0.19/0.54 left_division(X, left_division(left_inverse(X), multiply(identity, left_inverse(X))))
% 0.19/0.54 = { by axiom 2 (left_identity) }
% 0.19/0.54 left_division(X, left_division(left_inverse(X), left_inverse(X)))
% 0.19/0.54 = { by axiom 1 (right_identity) R->L }
% 0.19/0.54 left_division(X, left_division(left_inverse(X), multiply(left_inverse(X), identity)))
% 0.19/0.54 = { by axiom 7 (left_division_multiply) }
% 0.19/0.54 left_division(X, identity)
% 0.19/0.54 = { by lemma 11 }
% 0.19/0.54 right_inverse(X)
% 0.19/0.54
% 0.19/0.54 Lemma 13: right_division(multiply(X, multiply(Y, X)), X) = multiply(X, Y).
% 0.19/0.54 Proof:
% 0.19/0.54 right_division(multiply(X, multiply(Y, X)), X)
% 0.19/0.54 = { by lemma 10 R->L }
% 0.19/0.54 right_division(multiply(multiply(X, Y), X), X)
% 0.19/0.54 = { by axiom 8 (right_division_multiply) }
% 0.19/0.54 multiply(X, Y)
% 0.19/0.54
% 0.19/0.54 Lemma 14: right_division(X, multiply(Y, X)) = right_inverse(Y).
% 0.19/0.54 Proof:
% 0.19/0.54 right_division(X, multiply(Y, X))
% 0.19/0.54 = { by axiom 8 (right_division_multiply) R->L }
% 0.19/0.54 right_division(right_division(multiply(X, right_inverse(Y)), right_inverse(Y)), multiply(Y, X))
% 0.19/0.54 = { by lemma 12 R->L }
% 0.19/0.54 right_division(right_division(multiply(X, left_inverse(Y)), right_inverse(Y)), multiply(Y, X))
% 0.19/0.54 = { by axiom 2 (left_identity) R->L }
% 0.19/0.54 right_division(right_division(multiply(identity, multiply(X, left_inverse(Y))), right_inverse(Y)), multiply(Y, X))
% 0.19/0.54 = { by axiom 4 (left_inverse) R->L }
% 0.19/0.54 right_division(right_division(multiply(multiply(left_inverse(Y), Y), multiply(X, left_inverse(Y))), right_inverse(Y)), multiply(Y, X))
% 0.19/0.54 = { by axiom 9 (moufang1) R->L }
% 0.19/0.54 right_division(right_division(multiply(multiply(left_inverse(Y), multiply(Y, X)), left_inverse(Y)), right_inverse(Y)), multiply(Y, X))
% 0.19/0.54 = { by lemma 10 }
% 0.19/0.54 right_division(right_division(multiply(left_inverse(Y), multiply(multiply(Y, X), left_inverse(Y))), right_inverse(Y)), multiply(Y, X))
% 0.19/0.54 = { by lemma 12 }
% 0.19/0.54 right_division(right_division(multiply(left_inverse(Y), multiply(multiply(Y, X), right_inverse(Y))), right_inverse(Y)), multiply(Y, X))
% 0.19/0.54 = { by lemma 12 }
% 0.19/0.54 right_division(right_division(multiply(right_inverse(Y), multiply(multiply(Y, X), right_inverse(Y))), right_inverse(Y)), multiply(Y, X))
% 0.19/0.54 = { by lemma 13 }
% 0.19/0.54 right_division(multiply(right_inverse(Y), multiply(Y, X)), multiply(Y, X))
% 0.19/0.54 = { by axiom 8 (right_division_multiply) }
% 0.19/0.54 right_inverse(Y)
% 0.19/0.54
% 0.19/0.54 Lemma 15: multiply(X, multiply(right_inverse(X), Y)) = Y.
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(X, multiply(right_inverse(X), Y))
% 0.19/0.54 = { by axiom 8 (right_division_multiply) R->L }
% 0.19/0.54 right_division(multiply(multiply(X, multiply(right_inverse(X), Y)), left_division(multiply(X, multiply(right_inverse(X), Y)), multiply(Y, X))), left_division(multiply(X, multiply(right_inverse(X), Y)), multiply(Y, X)))
% 0.19/0.54 = { by axiom 5 (multiply_left_division) }
% 0.19/0.54 right_division(multiply(Y, X), left_division(multiply(X, multiply(right_inverse(X), Y)), multiply(Y, X)))
% 0.19/0.54 = { by axiom 2 (left_identity) R->L }
% 0.19/0.54 right_division(multiply(Y, X), left_division(multiply(X, multiply(right_inverse(X), Y)), multiply(identity, multiply(Y, X))))
% 0.19/0.54 = { by axiom 3 (right_inverse) R->L }
% 0.19/0.54 right_division(multiply(Y, X), left_division(multiply(X, multiply(right_inverse(X), Y)), multiply(multiply(X, right_inverse(X)), multiply(Y, X))))
% 0.19/0.54 = { by axiom 9 (moufang1) R->L }
% 0.19/0.54 right_division(multiply(Y, X), left_division(multiply(X, multiply(right_inverse(X), Y)), multiply(multiply(X, multiply(right_inverse(X), Y)), X)))
% 0.19/0.54 = { by axiom 7 (left_division_multiply) }
% 0.19/0.54 right_division(multiply(Y, X), X)
% 0.19/0.54 = { by axiom 8 (right_division_multiply) }
% 0.19/0.54 Y
% 0.19/0.54
% 0.19/0.54 Goal 1 (prove_moufang2): multiply(multiply(multiply(a, b), c), b) = multiply(a, multiply(b, multiply(c, b))).
% 0.19/0.54 Proof:
% 0.19/0.54 multiply(multiply(multiply(a, b), c), b)
% 0.19/0.54 = { by axiom 5 (multiply_left_division) R->L }
% 0.19/0.54 multiply(a, left_division(a, multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by axiom 7 (left_division_multiply) R->L }
% 0.19/0.55 multiply(a, left_division(left_division(left_inverse(a), multiply(left_inverse(a), a)), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by axiom 4 (left_inverse) }
% 0.19/0.55 multiply(a, left_division(left_division(left_inverse(a), identity), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by lemma 11 }
% 0.19/0.55 multiply(a, left_division(right_inverse(left_inverse(a)), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by axiom 8 (right_division_multiply) R->L }
% 0.19/0.55 multiply(a, right_division(multiply(left_division(right_inverse(left_inverse(a)), multiply(multiply(multiply(a, b), c), b)), left_inverse(a)), left_inverse(a)))
% 0.19/0.55 = { by axiom 2 (left_identity) R->L }
% 0.19/0.55 multiply(a, right_division(multiply(identity, multiply(left_division(right_inverse(left_inverse(a)), multiply(multiply(multiply(a, b), c), b)), left_inverse(a))), left_inverse(a)))
% 0.19/0.55 = { by axiom 3 (right_inverse) R->L }
% 0.19/0.55 multiply(a, right_division(multiply(multiply(left_inverse(a), right_inverse(left_inverse(a))), multiply(left_division(right_inverse(left_inverse(a)), multiply(multiply(multiply(a, b), c), b)), left_inverse(a))), left_inverse(a)))
% 0.19/0.55 = { by axiom 9 (moufang1) R->L }
% 0.19/0.55 multiply(a, right_division(multiply(multiply(left_inverse(a), multiply(right_inverse(left_inverse(a)), left_division(right_inverse(left_inverse(a)), multiply(multiply(multiply(a, b), c), b)))), left_inverse(a)), left_inverse(a)))
% 0.19/0.55 = { by axiom 5 (multiply_left_division) }
% 0.19/0.55 multiply(a, right_division(multiply(multiply(left_inverse(a), multiply(multiply(multiply(a, b), c), b)), left_inverse(a)), left_inverse(a)))
% 0.19/0.55 = { by lemma 10 }
% 0.19/0.55 multiply(a, right_division(multiply(left_inverse(a), multiply(multiply(multiply(multiply(a, b), c), b), left_inverse(a))), left_inverse(a)))
% 0.19/0.55 = { by lemma 13 }
% 0.19/0.55 multiply(a, multiply(left_inverse(a), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by lemma 12 }
% 0.19/0.55 multiply(a, multiply(right_inverse(a), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by lemma 14 R->L }
% 0.19/0.55 multiply(a, multiply(right_division(b, multiply(a, b)), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by lemma 15 R->L }
% 0.19/0.55 multiply(a, multiply(right_division(multiply(multiply(a, b), multiply(right_inverse(multiply(a, b)), b)), multiply(a, b)), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by axiom 1 (right_identity) R->L }
% 0.19/0.55 multiply(a, multiply(right_division(multiply(multiply(multiply(a, b), multiply(right_inverse(multiply(a, b)), b)), identity), multiply(a, b)), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by axiom 4 (left_inverse) R->L }
% 0.19/0.55 multiply(a, multiply(right_division(multiply(multiply(multiply(a, b), multiply(right_inverse(multiply(a, b)), b)), multiply(left_inverse(multiply(a, b)), multiply(a, b))), multiply(a, b)), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by axiom 9 (moufang1) R->L }
% 0.19/0.55 multiply(a, multiply(right_division(multiply(multiply(multiply(a, b), multiply(multiply(right_inverse(multiply(a, b)), b), left_inverse(multiply(a, b)))), multiply(a, b)), multiply(a, b)), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by axiom 8 (right_division_multiply) }
% 0.19/0.55 multiply(a, multiply(multiply(multiply(a, b), multiply(multiply(right_inverse(multiply(a, b)), b), left_inverse(multiply(a, b)))), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by lemma 12 }
% 0.19/0.55 multiply(a, multiply(multiply(multiply(a, b), multiply(multiply(right_inverse(multiply(a, b)), b), right_inverse(multiply(a, b)))), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by lemma 10 }
% 0.19/0.55 multiply(a, multiply(multiply(multiply(a, b), multiply(right_inverse(multiply(a, b)), multiply(b, right_inverse(multiply(a, b))))), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by lemma 15 }
% 0.19/0.55 multiply(a, multiply(multiply(b, right_inverse(multiply(a, b))), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by lemma 14 R->L }
% 0.19/0.55 multiply(a, multiply(multiply(b, right_division(c, multiply(multiply(a, b), c))), multiply(multiply(multiply(a, b), c), b)))
% 0.19/0.55 = { by axiom 9 (moufang1) R->L }
% 0.19/0.55 multiply(a, multiply(multiply(b, multiply(right_division(c, multiply(multiply(a, b), c)), multiply(multiply(a, b), c))), b))
% 0.19/0.55 = { by axiom 6 (multiply_right_division) }
% 0.19/0.55 multiply(a, multiply(multiply(b, c), b))
% 0.19/0.55 = { by lemma 10 }
% 0.19/0.55 multiply(a, multiply(b, multiply(c, b)))
% 0.19/0.55 % SZS output end Proof
% 0.19/0.55
% 0.19/0.55 RESULT: Unsatisfiable (the axioms are contradictory).
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