TSTP Solution File: REL031+2 by Twee---2.4.2
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- Process Solution
%------------------------------------------------------------------------------
% File : Twee---2.4.2
% Problem : REL031+2 : TPTP v8.1.2. Released v4.0.0.
% 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 : n027.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 13:44:16 EDT 2023
% Result : Theorem 0.22s 0.50s
% Output : Proof 0.22s
% 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 : REL031+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.19/0.35 % Computer : n027.cluster.edu
% 0.19/0.35 % Model : x86_64 x86_64
% 0.19/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.35 % Memory : 8042.1875MB
% 0.19/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.19/0.35 % CPULimit : 300
% 0.19/0.35 % WCLimit : 300
% 0.19/0.35 % DateTime : Fri Aug 25 19:30:49 EDT 2023
% 0.19/0.36 % CPUTime :
% 0.22/0.50 Command-line arguments: --set-join --lhs-weight 1 --no-flatten-goal --complete-subsets --goal-heuristic
% 0.22/0.50
% 0.22/0.50 % SZS status Theorem
% 0.22/0.50
% 0.22/0.50 % SZS output start Proof
% 0.22/0.50 Axiom 1 (converse_idempotence): converse(converse(X)) = X.
% 0.22/0.50 Axiom 2 (maddux1_join_commutativity): join(X, Y) = join(Y, X).
% 0.22/0.50 Axiom 3 (composition_identity): composition(X, one) = X.
% 0.22/0.50 Axiom 4 (converse_additivity): converse(join(X, Y)) = join(converse(X), converse(Y)).
% 0.22/0.50 Axiom 5 (maddux2_join_associativity): join(X, join(Y, Z)) = join(join(X, Y), Z).
% 0.22/0.50 Axiom 6 (converse_multiplicativity): converse(composition(X, Y)) = composition(converse(Y), converse(X)).
% 0.22/0.50 Axiom 7 (composition_associativity): composition(X, composition(Y, Z)) = composition(composition(X, Y), Z).
% 0.22/0.50 Axiom 8 (goals): join(composition(converse(x1), x1), one) = one.
% 0.22/0.50 Axiom 9 (goals_1): join(composition(converse(x0), x0), one) = one.
% 0.22/0.50 Axiom 10 (composition_distributivity): composition(join(X, Y), Z) = join(composition(X, Z), composition(Y, Z)).
% 0.22/0.50
% 0.22/0.50 Lemma 11: converse(composition(converse(X), Y)) = composition(converse(Y), X).
% 0.22/0.50 Proof:
% 0.22/0.50 converse(composition(converse(X), Y))
% 0.22/0.50 = { by axiom 6 (converse_multiplicativity) }
% 0.22/0.50 composition(converse(Y), converse(converse(X)))
% 0.22/0.50 = { by axiom 1 (converse_idempotence) }
% 0.22/0.51 composition(converse(Y), X)
% 0.22/0.51
% 0.22/0.51 Lemma 12: composition(converse(one), X) = X.
% 0.22/0.51 Proof:
% 0.22/0.51 composition(converse(one), X)
% 0.22/0.51 = { by lemma 11 R->L }
% 0.22/0.51 converse(composition(converse(X), one))
% 0.22/0.51 = { by axiom 3 (composition_identity) }
% 0.22/0.51 converse(converse(X))
% 0.22/0.51 = { by axiom 1 (converse_idempotence) }
% 0.22/0.51 X
% 0.22/0.51
% 0.22/0.51 Lemma 13: converse(one) = one.
% 0.22/0.51 Proof:
% 0.22/0.51 converse(one)
% 0.22/0.51 = { by axiom 3 (composition_identity) R->L }
% 0.22/0.51 composition(converse(one), one)
% 0.22/0.51 = { by lemma 12 }
% 0.22/0.51 one
% 0.22/0.51
% 0.22/0.51 Lemma 14: join(one, composition(converse(x1), x1)) = one.
% 0.22/0.51 Proof:
% 0.22/0.51 join(one, composition(converse(x1), x1))
% 0.22/0.51 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.22/0.51 join(composition(converse(x1), x1), one)
% 0.22/0.51 = { by axiom 8 (goals) }
% 0.22/0.51 one
% 0.22/0.51
% 0.22/0.51 Goal 1 (goals_2): join(composition(converse(composition(x0, x1)), composition(x0, x1)), one) = one.
% 0.22/0.51 Proof:
% 0.22/0.51 join(composition(converse(composition(x0, x1)), composition(x0, x1)), one)
% 0.22/0.51 = { by axiom 2 (maddux1_join_commutativity) }
% 0.22/0.51 join(one, composition(converse(composition(x0, x1)), composition(x0, x1)))
% 0.22/0.51 = { by axiom 7 (composition_associativity) }
% 0.22/0.51 join(one, composition(composition(converse(composition(x0, x1)), x0), x1))
% 0.22/0.51 = { by lemma 14 R->L }
% 0.22/0.51 join(join(one, composition(converse(x1), x1)), composition(composition(converse(composition(x0, x1)), x0), x1))
% 0.22/0.51 = { by axiom 5 (maddux2_join_associativity) R->L }
% 0.22/0.51 join(one, join(composition(converse(x1), x1), composition(composition(converse(composition(x0, x1)), x0), x1)))
% 0.22/0.51 = { by axiom 2 (maddux1_join_commutativity) }
% 0.22/0.51 join(one, join(composition(composition(converse(composition(x0, x1)), x0), x1), composition(converse(x1), x1)))
% 0.22/0.51 = { by axiom 10 (composition_distributivity) R->L }
% 0.22/0.51 join(one, composition(join(composition(converse(composition(x0, x1)), x0), converse(x1)), x1))
% 0.22/0.51 = { by axiom 2 (maddux1_join_commutativity) }
% 0.22/0.51 join(one, composition(join(converse(x1), composition(converse(composition(x0, x1)), x0)), x1))
% 0.22/0.51 = { by axiom 6 (converse_multiplicativity) }
% 0.22/0.51 join(one, composition(join(converse(x1), composition(composition(converse(x1), converse(x0)), x0)), x1))
% 0.22/0.51 = { by axiom 1 (converse_idempotence) R->L }
% 0.22/0.51 join(one, composition(join(converse(x1), composition(composition(converse(converse(converse(x1))), converse(x0)), x0)), x1))
% 0.22/0.51 = { by axiom 6 (converse_multiplicativity) R->L }
% 0.22/0.51 join(one, composition(join(converse(x1), composition(converse(composition(x0, converse(converse(x1)))), x0)), x1))
% 0.22/0.51 = { by lemma 11 R->L }
% 0.22/0.51 join(one, composition(join(converse(x1), converse(composition(converse(x0), composition(x0, converse(converse(x1)))))), x1))
% 0.22/0.51 = { by axiom 1 (converse_idempotence) R->L }
% 0.22/0.51 join(one, composition(join(converse(converse(converse(x1))), converse(composition(converse(x0), composition(x0, converse(converse(x1)))))), x1))
% 0.22/0.51 = { by axiom 4 (converse_additivity) R->L }
% 0.22/0.51 join(one, composition(converse(join(converse(converse(x1)), composition(converse(x0), composition(x0, converse(converse(x1)))))), x1))
% 0.22/0.51 = { by axiom 7 (composition_associativity) }
% 0.22/0.51 join(one, composition(converse(join(converse(converse(x1)), composition(composition(converse(x0), x0), converse(converse(x1))))), x1))
% 0.22/0.51 = { by lemma 12 R->L }
% 0.22/0.51 join(one, composition(converse(join(composition(converse(one), converse(converse(x1))), composition(composition(converse(x0), x0), converse(converse(x1))))), x1))
% 0.22/0.51 = { by axiom 10 (composition_distributivity) R->L }
% 0.22/0.51 join(one, composition(converse(composition(join(converse(one), composition(converse(x0), x0)), converse(converse(x1)))), x1))
% 0.22/0.51 = { by lemma 13 }
% 0.22/0.51 join(one, composition(converse(composition(join(one, composition(converse(x0), x0)), converse(converse(x1)))), x1))
% 0.22/0.51 = { by axiom 2 (maddux1_join_commutativity) R->L }
% 0.22/0.51 join(one, composition(converse(composition(join(composition(converse(x0), x0), one), converse(converse(x1)))), x1))
% 0.22/0.51 = { by axiom 9 (goals_1) }
% 0.22/0.51 join(one, composition(converse(composition(one, converse(converse(x1)))), x1))
% 0.22/0.51 = { by lemma 13 R->L }
% 0.22/0.51 join(one, composition(converse(composition(converse(one), converse(converse(x1)))), x1))
% 0.22/0.51 = { by lemma 12 }
% 0.22/0.51 join(one, composition(converse(converse(converse(x1))), x1))
% 0.22/0.51 = { by axiom 1 (converse_idempotence) }
% 0.22/0.51 join(one, composition(converse(x1), x1))
% 0.22/0.51 = { by lemma 14 }
% 0.22/0.51 one
% 0.22/0.51 % SZS output end Proof
% 0.22/0.51
% 0.22/0.51 RESULT: Theorem (the conjecture is true).
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