%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : REL008+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 : Sat Jun 21 05:23:39 AM UTC 2025
% Result : Theorem 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : REL008+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n016.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 02:49:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.38 % SZS status Theorem
% 0.12/0.38 % SZS output start Proof
% 0.12/0.38 tff(join_type, type, (
% 0.12/0.38 join: ( $i * $i ) > $i)).
% 0.12/0.38 tff(composition_type, type, (
% 0.12/0.38 composition: ( $i * $i ) > $i)).
% 0.12/0.38 tff(tptp_fun_X2_0_type, type, (
% 0.12/0.38 tptp_fun_X2_0: $i)).
% 0.12/0.38 tff(tptp_fun_X0_2_type, type, (
% 0.12/0.38 tptp_fun_X0_2: $i)).
% 0.12/0.38 tff(tptp_fun_X1_1_type, type, (
% 0.12/0.38 tptp_fun_X1_1: $i)).
% 0.12/0.38 tff(converse_type, type, (
% 0.12/0.38 converse: $i > $i)).
% 0.12/0.38 tff(1,plain,
% 0.12/0.38 (^[X0: $i, X1: $i] : refl((join(X0, X1) = join(X1, X0)) <=> (join(X0, X1) = join(X1, X0)))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(2,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0)) <=> ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[1])).
% 0.12/0.38 tff(3,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0)) <=> ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(4,axiom,(![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))), file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax','maddux1_join_commutativity')).
% 0.12/0.38 tff(5,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.38 tff(6,plain,(
% 0.12/0.38 ![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 0.12/0.38 inference(skolemize,[status(sab)],[5])).
% 0.12/0.38 tff(7,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.12/0.38 tff(8,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : (join(X0, X1) = join(X1, X0))) | (join(composition(X0!2, X1!1), composition(X0!2, X2!0)) = join(composition(X0!2, X2!0), composition(X0!2, X1!1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(9,plain,
% 0.12/0.38 (join(composition(X0!2, X1!1), composition(X0!2, X2!0)) = join(composition(X0!2, X2!0), composition(X0!2, X1!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.12/0.38 tff(10,plain,
% 0.12/0.38 (join(composition(X0!2, X2!0), composition(X0!2, X1!1)) = join(composition(X0!2, X1!1), composition(X0!2, X2!0))),
% 0.12/0.38 inference(symmetry,[status(thm)],[9])).
% 0.12/0.38 tff(11,plain,
% 0.12/0.38 (![X0: $i] : (converse(converse(X0)) = X0) <=> ![X0: $i] : (converse(converse(X0)) = X0)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(12,plain,
% 0.12/0.38 (![X0: $i] : (converse(converse(X0)) = X0) <=> ![X0: $i] : (converse(converse(X0)) = X0)),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(13,axiom,(![X0: $i] : (converse(converse(X0)) = X0)), file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax','converse_idempotence')).
% 0.12/0.38 tff(14,plain,
% 0.12/0.38 (![X0: $i] : (converse(converse(X0)) = X0)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[13, 12])).
% 0.12/0.38 tff(15,plain,(
% 0.12/0.38 ![X0: $i] : (converse(converse(X0)) = X0)),
% 0.12/0.38 inference(skolemize,[status(sab)],[14])).
% 0.12/0.38 tff(16,plain,
% 0.12/0.38 (![X0: $i] : (converse(converse(X0)) = X0)),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.12/0.38 tff(17,plain,
% 0.12/0.38 ((~![X0: $i] : (converse(converse(X0)) = X0)) | (converse(converse(join(composition(X0!2, X2!0), composition(X0!2, X1!1)))) = join(composition(X0!2, X2!0), composition(X0!2, X1!1)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(18,plain,
% 0.12/0.38 (converse(converse(join(composition(X0!2, X2!0), composition(X0!2, X1!1)))) = join(composition(X0!2, X2!0), composition(X0!2, X1!1))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[17, 16])).
% 0.12/0.38 tff(19,plain,
% 0.12/0.38 (^[X0: $i, X1: $i] : refl((converse(composition(X0, X1)) = composition(converse(X1), converse(X0))) <=> (converse(composition(X0, X1)) = composition(converse(X1), converse(X0))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(20,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (converse(composition(X0, X1)) = composition(converse(X1), converse(X0))) <=> ![X0: $i, X1: $i] : (converse(composition(X0, X1)) = composition(converse(X1), converse(X0)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[19])).
% 0.12/0.38 tff(21,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (converse(composition(X0, X1)) = composition(converse(X1), converse(X0))) <=> ![X0: $i, X1: $i] : (converse(composition(X0, X1)) = composition(converse(X1), converse(X0)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(22,axiom,(![X0: $i, X1: $i] : (converse(composition(X0, X1)) = composition(converse(X1), converse(X0)))), file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax','converse_multiplicativity')).
% 0.12/0.38 tff(23,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (converse(composition(X0, X1)) = composition(converse(X1), converse(X0)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[22, 21])).
% 0.12/0.38 tff(24,plain,(
% 0.12/0.38 ![X0: $i, X1: $i] : (converse(composition(X0, X1)) = composition(converse(X1), converse(X0)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[23])).
% 0.12/0.38 tff(25,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (converse(composition(X0, X1)) = composition(converse(X1), converse(X0)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[24, 20])).
% 0.12/0.38 tff(26,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : (converse(composition(X0, X1)) = composition(converse(X1), converse(X0)))) | (converse(composition(X0!2, X2!0)) = composition(converse(X2!0), converse(X0!2)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(27,plain,
% 0.12/0.38 (converse(composition(X0!2, X2!0)) = composition(converse(X2!0), converse(X0!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[26, 25])).
% 0.12/0.38 tff(28,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : (converse(composition(X0, X1)) = composition(converse(X1), converse(X0)))) | (converse(composition(X0!2, X1!1)) = composition(converse(X1!1), converse(X0!2)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(29,plain,
% 0.12/0.38 (converse(composition(X0!2, X1!1)) = composition(converse(X1!1), converse(X0!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[28, 25])).
% 0.12/0.38 tff(30,plain,
% 0.12/0.38 (join(converse(composition(X0!2, X1!1)), converse(composition(X0!2, X2!0))) = join(composition(converse(X1!1), converse(X0!2)), composition(converse(X2!0), converse(X0!2)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[29, 27])).
% 0.12/0.38 tff(31,plain,
% 0.12/0.38 (^[X0: $i, X1: $i] : refl((converse(join(X0, X1)) = join(converse(X0), converse(X1))) <=> (converse(join(X0, X1)) = join(converse(X0), converse(X1))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(32,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1))) <=> ![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[31])).
% 0.12/0.38 tff(33,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1))) <=> ![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(34,axiom,(![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))), file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax','converse_additivity')).
% 0.12/0.38 tff(35,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[34, 33])).
% 0.12/0.38 tff(36,plain,(
% 0.12/0.38 ![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[35])).
% 0.12/0.38 tff(37,plain,
% 0.12/0.38 (![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[36, 32])).
% 0.12/0.38 tff(38,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))) | (converse(join(composition(X0!2, X1!1), composition(X0!2, X2!0))) = join(converse(composition(X0!2, X1!1)), converse(composition(X0!2, X2!0))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(39,plain,
% 0.12/0.38 (converse(join(composition(X0!2, X1!1), composition(X0!2, X2!0))) = join(converse(composition(X0!2, X1!1)), converse(composition(X0!2, X2!0)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[38, 37])).
% 0.12/0.38 tff(40,plain,
% 0.12/0.38 (converse(join(composition(X0!2, X2!0), composition(X0!2, X1!1))) = converse(join(composition(X0!2, X1!1), composition(X0!2, X2!0)))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[10])).
% 0.12/0.38 tff(41,plain,
% 0.12/0.38 (converse(join(composition(X0!2, X2!0), composition(X0!2, X1!1))) = join(composition(converse(X1!1), converse(X0!2)), composition(converse(X2!0), converse(X0!2)))),
% 0.12/0.38 inference(transitivity,[status(thm)],[40, 39, 30])).
% 0.12/0.38 tff(42,plain,
% 0.12/0.38 (converse(converse(join(composition(X0!2, X2!0), composition(X0!2, X1!1)))) = converse(join(composition(converse(X1!1), converse(X0!2)), composition(converse(X2!0), converse(X0!2))))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[41])).
% 0.12/0.38 tff(43,plain,
% 0.12/0.38 (converse(join(composition(converse(X1!1), converse(X0!2)), composition(converse(X2!0), converse(X0!2)))) = converse(converse(join(composition(X0!2, X2!0), composition(X0!2, X1!1))))),
% 0.12/0.38 inference(symmetry,[status(thm)],[42])).
% 0.12/0.38 tff(44,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : (converse(composition(X0, X1)) = composition(converse(X1), converse(X0)))) | (converse(composition(X0!2, join(X1!1, X2!0))) = composition(converse(join(X1!1, X2!0)), converse(X0!2)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(45,plain,
% 0.12/0.38 (converse(composition(X0!2, join(X1!1, X2!0))) = composition(converse(join(X1!1, X2!0)), converse(X0!2))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[44, 25])).
% 0.12/0.38 tff(46,plain,
% 0.12/0.38 (composition(converse(join(X1!1, X2!0)), converse(X0!2)) = converse(composition(X0!2, join(X1!1, X2!0)))),
% 0.12/0.38 inference(symmetry,[status(thm)],[45])).
% 0.12/0.38 tff(47,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i] : (converse(join(X0, X1)) = join(converse(X0), converse(X1)))) | (converse(join(X1!1, X2!0)) = join(converse(X1!1), converse(X2!0)))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(48,plain,
% 0.12/0.38 (converse(join(X1!1, X2!0)) = join(converse(X1!1), converse(X2!0))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[47, 37])).
% 0.12/0.38 tff(49,plain,
% 0.12/0.38 (composition(converse(join(X1!1, X2!0)), converse(X0!2)) = composition(join(converse(X1!1), converse(X2!0)), converse(X0!2))),
% 0.12/0.38 inference(monotonicity,[status(thm)],[48])).
% 0.12/0.38 tff(50,plain,
% 0.12/0.38 (composition(join(converse(X1!1), converse(X2!0)), converse(X0!2)) = composition(converse(join(X1!1, X2!0)), converse(X0!2))),
% 0.12/0.38 inference(symmetry,[status(thm)],[49])).
% 0.12/0.38 tff(51,plain,
% 0.12/0.38 (^[X0: $i, X1: $i, X2: $i] : refl((composition(join(X0, X1), X2) = join(composition(X0, X2), composition(X1, X2))) <=> (composition(join(X0, X1), X2) = join(composition(X0, X2), composition(X1, X2))))),
% 0.12/0.38 inference(bind,[status(th)],[])).
% 0.12/0.38 tff(52,plain,
% 0.12/0.38 (![X0: $i, X1: $i, X2: $i] : (composition(join(X0, X1), X2) = join(composition(X0, X2), composition(X1, X2))) <=> ![X0: $i, X1: $i, X2: $i] : (composition(join(X0, X1), X2) = join(composition(X0, X2), composition(X1, X2)))),
% 0.12/0.38 inference(quant_intro,[status(thm)],[51])).
% 0.12/0.38 tff(53,plain,
% 0.12/0.38 (![X0: $i, X1: $i, X2: $i] : (composition(join(X0, X1), X2) = join(composition(X0, X2), composition(X1, X2))) <=> ![X0: $i, X1: $i, X2: $i] : (composition(join(X0, X1), X2) = join(composition(X0, X2), composition(X1, X2)))),
% 0.12/0.38 inference(rewrite,[status(thm)],[])).
% 0.12/0.38 tff(54,axiom,(![X0: $i, X1: $i, X2: $i] : (composition(join(X0, X1), X2) = join(composition(X0, X2), composition(X1, X2)))), file('/export/starexec/sandbox/benchmark/Axioms/REL001+0.ax','composition_distributivity')).
% 0.12/0.38 tff(55,plain,
% 0.12/0.38 (![X0: $i, X1: $i, X2: $i] : (composition(join(X0, X1), X2) = join(composition(X0, X2), composition(X1, X2)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.12/0.38 tff(56,plain,(
% 0.12/0.38 ![X0: $i, X1: $i, X2: $i] : (composition(join(X0, X1), X2) = join(composition(X0, X2), composition(X1, X2)))),
% 0.12/0.38 inference(skolemize,[status(sab)],[55])).
% 0.12/0.38 tff(57,plain,
% 0.12/0.38 (![X0: $i, X1: $i, X2: $i] : (composition(join(X0, X1), X2) = join(composition(X0, X2), composition(X1, X2)))),
% 0.12/0.38 inference(modus_ponens,[status(thm)],[56, 52])).
% 0.12/0.38 tff(58,plain,
% 0.12/0.38 ((~![X0: $i, X1: $i, X2: $i] : (composition(join(X0, X1), X2) = join(composition(X0, X2), composition(X1, X2)))) | (composition(join(converse(X1!1), converse(X2!0)), converse(X0!2)) = join(composition(converse(X1!1), converse(X0!2)), composition(converse(X2!0), converse(X0!2))))),
% 0.12/0.38 inference(quant_inst,[status(thm)],[])).
% 0.12/0.38 tff(59,plain,
% 0.12/0.38 (composition(join(converse(X1!1), converse(X2!0)), converse(X0!2)) = join(composition(converse(X1!1), converse(X0!2)), composition(converse(X2!0), converse(X0!2)))),
% 0.12/0.38 inference(unit_resolution,[status(thm)],[58, 57])).
% 0.12/0.38 tff(60,plain,
% 0.12/0.38 (join(composition(converse(X1!1), converse(X0!2)), composition(converse(X2!0), converse(X0!2))) = composition(join(converse(X1!1), converse(X2!0)), converse(X0!2))),
% 0.12/0.38 inference(symmetry,[status(thm)],[59])).
% 0.12/0.38 tff(61,plain,
% 0.12/0.38 (join(composition(converse(X1!1), converse(X0!2)), composition(converse(X2!0), converse(X0!2))) = converse(composition(X0!2, join(X1!1, X2!0)))),
% 0.12/0.39 inference(transitivity,[status(thm)],[60, 50, 46])).
% 0.12/0.39 tff(62,plain,
% 0.12/0.39 (converse(join(composition(converse(X1!1), converse(X0!2)), composition(converse(X2!0), converse(X0!2)))) = converse(converse(composition(X0!2, join(X1!1, X2!0))))),
% 0.12/0.39 inference(monotonicity,[status(thm)],[61])).
% 0.12/0.39 tff(63,plain,
% 0.12/0.39 (converse(converse(composition(X0!2, join(X1!1, X2!0)))) = converse(join(composition(converse(X1!1), converse(X0!2)), composition(converse(X2!0), converse(X0!2))))),
% 0.12/0.39 inference(symmetry,[status(thm)],[62])).
% 0.12/0.39 tff(64,plain,
% 0.12/0.39 ((~![X0: $i] : (converse(converse(X0)) = X0)) | (converse(converse(composition(X0!2, join(X1!1, X2!0)))) = composition(X0!2, join(X1!1, X2!0)))),
% 0.12/0.39 inference(quant_inst,[status(thm)],[])).
% 0.12/0.39 tff(65,plain,
% 0.12/0.39 (converse(converse(composition(X0!2, join(X1!1, X2!0)))) = composition(X0!2, join(X1!1, X2!0))),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[64, 16])).
% 0.12/0.39 tff(66,plain,
% 0.12/0.39 (composition(X0!2, join(X1!1, X2!0)) = converse(converse(composition(X0!2, join(X1!1, X2!0))))),
% 0.12/0.39 inference(symmetry,[status(thm)],[65])).
% 0.12/0.39 tff(67,plain,
% 0.12/0.39 (composition(X0!2, join(X1!1, X2!0)) = join(composition(X0!2, X1!1), composition(X0!2, X2!0))),
% 0.12/0.39 inference(transitivity,[status(thm)],[66, 63, 43, 18, 10])).
% 0.12/0.39 tff(68,plain,
% 0.12/0.39 ((~![X0: $i, X1: $i, X2: $i] : (composition(X0, join(X1, X2)) = join(composition(X0, X1), composition(X0, X2)))) <=> (~![X0: $i, X1: $i, X2: $i] : (composition(X0, join(X1, X2)) = join(composition(X0, X1), composition(X0, X2))))),
% 0.12/0.39 inference(rewrite,[status(thm)],[])).
% 0.12/0.39 tff(69,axiom,(~![X0: $i, X1: $i, X2: $i] : (composition(X0, join(X1, X2)) = join(composition(X0, X1), composition(X0, X2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','goals')).
% 0.12/0.39 tff(70,plain,
% 0.12/0.39 (~![X0: $i, X1: $i, X2: $i] : (composition(X0, join(X1, X2)) = join(composition(X0, X1), composition(X0, X2)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.12/0.39 tff(71,plain,
% 0.12/0.39 (~![X0: $i, X1: $i, X2: $i] : (composition(X0, join(X1, X2)) = join(composition(X0, X1), composition(X0, X2)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[70, 68])).
% 0.12/0.39 tff(72,plain,
% 0.12/0.39 (~![X0: $i, X1: $i, X2: $i] : (composition(X0, join(X1, X2)) = join(composition(X0, X1), composition(X0, X2)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[71, 68])).
% 0.12/0.39 tff(73,plain,
% 0.12/0.39 (~![X0: $i, X1: $i, X2: $i] : (composition(X0, join(X1, X2)) = join(composition(X0, X1), composition(X0, X2)))),
% 0.12/0.39 inference(modus_ponens,[status(thm)],[72, 68])).
% 0.12/0.39 tff(74,plain,(
% 0.12/0.39 ~(composition(X0!2, join(X1!1, X2!0)) = join(composition(X0!2, X1!1), composition(X0!2, X2!0)))),
% 0.12/0.39 inference(skolemize,[status(sab)],[73])).
% 0.12/0.39 tff(75,plain,
% 0.12/0.39 ($false),
% 0.12/0.39 inference(unit_resolution,[status(thm)],[74, 67])).
% 0.12/0.39 % SZS output end Proof
% 0.12/0.39 % E exiting
%------------------------------------------------------------------------------