TSTP Solution File: GRP201-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP201-1 : 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 : n024.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 0.51s
% 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
% 0.06/0.12 % Problem : GRP201-1 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.13 % 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 : n024.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 : Mon Aug 28 20:02:53 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.51 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.19/0.51
% 0.19/0.51 % SZS status Unsatisfiable
% 0.19/0.51
% 0.19/0.52 % SZS output start Proof
% 0.19/0.52 Axiom 1 (right_identity): multiply(X, identity) = X.
% 0.19/0.52 Axiom 2 (left_identity): multiply(identity, X) = X.
% 0.19/0.52 Axiom 3 (right_inverse): multiply(X, right_inverse(X)) = identity.
% 0.19/0.52 Axiom 4 (left_inverse): multiply(left_inverse(X), X) = identity.
% 0.19/0.52 Axiom 5 (multiply_left_division): multiply(X, left_division(X, Y)) = Y.
% 0.19/0.52 Axiom 6 (multiply_right_division): multiply(right_division(X, Y), Y) = X.
% 0.19/0.52 Axiom 7 (left_division_multiply): left_division(X, multiply(X, Y)) = Y.
% 0.19/0.52 Axiom 8 (right_division_multiply): right_division(multiply(X, Y), Y) = X.
% 0.19/0.52 Axiom 9 (moufang2): multiply(multiply(multiply(X, Y), Z), Y) = multiply(X, multiply(Y, multiply(Z, Y))).
% 0.19/0.52
% 0.19/0.52 Lemma 10: multiply(left_inverse(X), multiply(X, Y)) = Y.
% 0.19/0.52 Proof:
% 0.19/0.52 multiply(left_inverse(X), multiply(X, Y))
% 0.19/0.52 = { by axiom 6 (multiply_right_division) R->L }
% 0.19/0.52 multiply(left_inverse(X), multiply(X, multiply(right_division(Y, X), X)))
% 0.19/0.52 = { by axiom 9 (moufang2) R->L }
% 0.19/0.52 multiply(multiply(multiply(left_inverse(X), X), right_division(Y, X)), X)
% 0.19/0.52 = { by axiom 4 (left_inverse) }
% 0.19/0.52 multiply(multiply(identity, right_division(Y, X)), X)
% 0.19/0.52 = { by axiom 2 (left_identity) }
% 0.19/0.52 multiply(right_division(Y, X), X)
% 0.19/0.52 = { by axiom 6 (multiply_right_division) }
% 0.19/0.52 Y
% 0.19/0.52
% 0.19/0.52 Lemma 11: left_inverse(X) = right_inverse(X).
% 0.19/0.52 Proof:
% 0.19/0.52 left_inverse(X)
% 0.19/0.52 = { by axiom 1 (right_identity) R->L }
% 0.19/0.52 multiply(left_inverse(X), identity)
% 0.19/0.52 = { by axiom 3 (right_inverse) R->L }
% 0.19/0.52 multiply(left_inverse(X), multiply(X, right_inverse(X)))
% 0.19/0.52 = { by lemma 10 }
% 0.19/0.52 right_inverse(X)
% 0.19/0.52
% 0.19/0.52 Lemma 12: multiply(right_inverse(X), Y) = left_division(X, Y).
% 0.19/0.52 Proof:
% 0.19/0.52 multiply(right_inverse(X), Y)
% 0.19/0.52 = { by lemma 11 R->L }
% 0.19/0.52 multiply(left_inverse(X), Y)
% 0.19/0.52 = { by axiom 5 (multiply_left_division) R->L }
% 0.19/0.52 multiply(left_inverse(X), multiply(X, left_division(X, Y)))
% 0.19/0.52 = { by lemma 10 }
% 0.19/0.52 left_division(X, Y)
% 0.19/0.52
% 0.19/0.52 Lemma 13: multiply(multiply(X, Y), right_inverse(Y)) = X.
% 0.19/0.52 Proof:
% 0.19/0.52 multiply(multiply(X, Y), right_inverse(Y))
% 0.19/0.52 = { by axiom 8 (right_division_multiply) R->L }
% 0.19/0.52 right_division(multiply(multiply(multiply(X, Y), right_inverse(Y)), Y), Y)
% 0.19/0.52 = { by lemma 11 R->L }
% 0.19/0.52 right_division(multiply(multiply(multiply(X, Y), left_inverse(Y)), Y), Y)
% 0.19/0.52 = { by axiom 9 (moufang2) }
% 0.19/0.52 right_division(multiply(X, multiply(Y, multiply(left_inverse(Y), Y))), Y)
% 0.19/0.52 = { by axiom 4 (left_inverse) }
% 0.19/0.52 right_division(multiply(X, multiply(Y, identity)), Y)
% 0.19/0.52 = { by axiom 1 (right_identity) }
% 0.19/0.52 right_division(multiply(X, Y), Y)
% 0.19/0.52 = { by axiom 8 (right_division_multiply) }
% 0.19/0.52 X
% 0.19/0.52
% 0.19/0.52 Lemma 14: left_division(multiply(X, Y), X) = right_inverse(Y).
% 0.19/0.52 Proof:
% 0.19/0.52 left_division(multiply(X, Y), X)
% 0.19/0.52 = { by lemma 13 R->L }
% 0.19/0.52 left_division(multiply(X, Y), multiply(multiply(X, Y), right_inverse(Y)))
% 0.19/0.52 = { by axiom 7 (left_division_multiply) }
% 0.19/0.52 right_inverse(Y)
% 0.19/0.52
% 0.19/0.52 Goal 1 (prove_moufang3): multiply(multiply(multiply(a, b), a), c) = multiply(a, multiply(b, multiply(a, c))).
% 0.19/0.52 Proof:
% 0.19/0.52 multiply(multiply(multiply(a, b), a), c)
% 0.19/0.53 = { by axiom 8 (right_division_multiply) R->L }
% 0.19/0.53 right_division(multiply(multiply(multiply(multiply(a, b), a), c), right_inverse(c)), right_inverse(c))
% 0.19/0.53 = { by lemma 13 }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), right_inverse(c))
% 0.19/0.53 = { by lemma 14 R->L }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), left_division(multiply(a, c), a))
% 0.19/0.53 = { by lemma 12 R->L }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), multiply(right_inverse(multiply(a, c)), a))
% 0.19/0.53 = { by lemma 14 R->L }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), multiply(left_division(multiply(b, multiply(a, c)), b), a))
% 0.19/0.53 = { by lemma 12 R->L }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), multiply(multiply(right_inverse(multiply(b, multiply(a, c))), b), a))
% 0.19/0.53 = { by axiom 6 (multiply_right_division) R->L }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), multiply(multiply(multiply(right_division(right_inverse(multiply(b, multiply(a, c))), a), a), b), a))
% 0.19/0.53 = { by axiom 9 (moufang2) }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), multiply(right_division(right_inverse(multiply(b, multiply(a, c))), a), multiply(a, multiply(b, a))))
% 0.19/0.53 = { by axiom 2 (left_identity) R->L }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), multiply(right_division(right_inverse(multiply(b, multiply(a, c))), a), multiply(identity, multiply(a, multiply(b, a)))))
% 0.19/0.53 = { by axiom 9 (moufang2) R->L }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), multiply(right_division(right_inverse(multiply(b, multiply(a, c))), a), multiply(multiply(multiply(identity, a), b), a)))
% 0.19/0.53 = { by axiom 2 (left_identity) }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), multiply(right_division(right_inverse(multiply(b, multiply(a, c))), a), multiply(multiply(a, b), a)))
% 0.19/0.53 = { by lemma 13 R->L }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), multiply(right_division(right_inverse(multiply(b, multiply(a, c))), multiply(multiply(a, multiply(b, multiply(a, c))), right_inverse(multiply(b, multiply(a, c))))), multiply(multiply(a, b), a)))
% 0.19/0.53 = { by lemma 10 R->L }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), multiply(right_division(multiply(left_inverse(multiply(a, multiply(b, multiply(a, c)))), multiply(multiply(a, multiply(b, multiply(a, c))), right_inverse(multiply(b, multiply(a, c))))), multiply(multiply(a, multiply(b, multiply(a, c))), right_inverse(multiply(b, multiply(a, c))))), multiply(multiply(a, b), a)))
% 0.19/0.53 = { by axiom 8 (right_division_multiply) }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), multiply(left_inverse(multiply(a, multiply(b, multiply(a, c)))), multiply(multiply(a, b), a)))
% 0.19/0.53 = { by lemma 11 }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), multiply(right_inverse(multiply(a, multiply(b, multiply(a, c)))), multiply(multiply(a, b), a)))
% 0.19/0.53 = { by lemma 12 }
% 0.19/0.53 right_division(multiply(multiply(a, b), a), left_division(multiply(a, multiply(b, multiply(a, c))), multiply(multiply(a, b), a)))
% 0.19/0.53 = { by axiom 5 (multiply_left_division) R->L }
% 0.19/0.53 right_division(multiply(multiply(a, multiply(b, multiply(a, c))), left_division(multiply(a, multiply(b, multiply(a, c))), multiply(multiply(a, b), a))), left_division(multiply(a, multiply(b, multiply(a, c))), multiply(multiply(a, b), a)))
% 0.19/0.53 = { by axiom 8 (right_division_multiply) }
% 0.19/0.53 multiply(a, multiply(b, multiply(a, c)))
% 0.19/0.53 % SZS output end Proof
% 0.19/0.53
% 0.19/0.53 RESULT: Unsatisfiable (the axioms are contradictory).
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