TSTP Solution File: GRP202-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : GRP202-1 : 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 : n001.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 0.21s 0.49s
% 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
% 0.00/0.12 % Problem : GRP202-1 : 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
% 0.14/0.34 % Computer : n001.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 : Tue Aug 29 03:12:36 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.49 Command-line arguments: --lhs-weight 1 --flip-ordering --normalise-queue-percent 10 --cp-renormalise-threshold 10
% 0.21/0.49
% 0.21/0.49 % SZS status Unsatisfiable
% 0.21/0.49
% 0.21/0.49 % SZS output start Proof
% 0.21/0.49 Axiom 1 (right_identity): multiply(X, identity) = X.
% 0.21/0.49 Axiom 2 (left_identity): multiply(identity, X) = X.
% 0.21/0.49 Axiom 3 (right_inverse): multiply(X, right_inverse(X)) = identity.
% 0.21/0.49 Axiom 4 (multiply_left_division): multiply(X, left_division(X, Y)) = Y.
% 0.21/0.49 Axiom 5 (multiply_right_division): multiply(right_division(X, Y), Y) = X.
% 0.21/0.49 Axiom 6 (left_division_multiply): left_division(X, multiply(X, Y)) = Y.
% 0.21/0.49 Axiom 7 (moufang3): multiply(multiply(multiply(X, Y), X), Z) = multiply(X, multiply(Y, multiply(X, Z))).
% 0.21/0.49
% 0.21/0.49 Lemma 8: multiply(multiply(X, Y), right_inverse(Y)) = X.
% 0.21/0.49 Proof:
% 0.21/0.49 multiply(multiply(X, Y), right_inverse(Y))
% 0.21/0.49 = { by axiom 4 (multiply_left_division) R->L }
% 0.21/0.49 multiply(multiply(multiply(Y, left_division(Y, X)), Y), right_inverse(Y))
% 0.21/0.49 = { by axiom 7 (moufang3) }
% 0.21/0.49 multiply(Y, multiply(left_division(Y, X), multiply(Y, right_inverse(Y))))
% 0.21/0.49 = { by axiom 3 (right_inverse) }
% 0.21/0.49 multiply(Y, multiply(left_division(Y, X), identity))
% 0.21/0.49 = { by axiom 1 (right_identity) }
% 0.21/0.49 multiply(Y, left_division(Y, X))
% 0.21/0.49 = { by axiom 4 (multiply_left_division) }
% 0.21/0.49 X
% 0.21/0.49
% 0.21/0.49 Goal 1 (prove_moufang1): multiply(multiply(a, multiply(b, c)), a) = multiply(multiply(a, b), multiply(c, a)).
% 0.21/0.49 Proof:
% 0.21/0.49 multiply(multiply(a, multiply(b, c)), a)
% 0.21/0.49 = { by axiom 5 (multiply_right_division) R->L }
% 0.21/0.49 multiply(right_division(multiply(multiply(a, multiply(b, c)), a), multiply(c, a)), multiply(c, a))
% 0.21/0.49 = { by lemma 8 R->L }
% 0.21/0.49 multiply(multiply(multiply(right_division(multiply(multiply(a, multiply(b, c)), a), multiply(c, a)), multiply(c, a)), right_inverse(multiply(c, a))), multiply(c, a))
% 0.21/0.49 = { by axiom 5 (multiply_right_division) }
% 0.21/0.49 multiply(multiply(multiply(multiply(a, multiply(b, c)), a), right_inverse(multiply(c, a))), multiply(c, a))
% 0.21/0.49 = { by axiom 6 (left_division_multiply) R->L }
% 0.21/0.49 multiply(multiply(multiply(multiply(a, multiply(b, c)), a), left_division(multiply(right_inverse(c), multiply(c, a)), multiply(multiply(right_inverse(c), multiply(c, a)), right_inverse(multiply(c, a))))), multiply(c, a))
% 0.21/0.49 = { by lemma 8 }
% 0.21/0.49 multiply(multiply(multiply(multiply(a, multiply(b, c)), a), left_division(multiply(right_inverse(c), multiply(c, a)), right_inverse(c))), multiply(c, a))
% 0.21/0.49 = { by axiom 6 (left_division_multiply) R->L }
% 0.21/0.49 multiply(multiply(multiply(multiply(a, multiply(b, c)), a), left_division(left_division(c, multiply(c, multiply(right_inverse(c), multiply(c, a)))), right_inverse(c))), multiply(c, a))
% 0.21/0.49 = { by axiom 7 (moufang3) R->L }
% 0.21/0.49 multiply(multiply(multiply(multiply(a, multiply(b, c)), a), left_division(left_division(c, multiply(multiply(multiply(c, right_inverse(c)), c), a)), right_inverse(c))), multiply(c, a))
% 0.21/0.49 = { by axiom 3 (right_inverse) }
% 0.21/0.49 multiply(multiply(multiply(multiply(a, multiply(b, c)), a), left_division(left_division(c, multiply(multiply(identity, c), a)), right_inverse(c))), multiply(c, a))
% 0.21/0.49 = { by axiom 2 (left_identity) }
% 0.21/0.49 multiply(multiply(multiply(multiply(a, multiply(b, c)), a), left_division(left_division(c, multiply(c, a)), right_inverse(c))), multiply(c, a))
% 0.21/0.49 = { by axiom 6 (left_division_multiply) }
% 0.21/0.49 multiply(multiply(multiply(multiply(a, multiply(b, c)), a), left_division(a, right_inverse(c))), multiply(c, a))
% 0.21/0.49 = { by axiom 7 (moufang3) }
% 0.21/0.49 multiply(multiply(a, multiply(multiply(b, c), multiply(a, left_division(a, right_inverse(c))))), multiply(c, a))
% 0.21/0.49 = { by axiom 4 (multiply_left_division) }
% 0.21/0.49 multiply(multiply(a, multiply(multiply(b, c), right_inverse(c))), multiply(c, a))
% 0.21/0.49 = { by lemma 8 }
% 0.21/0.49 multiply(multiply(a, b), multiply(c, a))
% 0.21/0.49 % SZS output end Proof
% 0.21/0.49
% 0.21/0.49 RESULT: Unsatisfiable (the axioms are contradictory).
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