%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA126-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% 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 : Tue May 5 06:33:44 PM UTC 2026
% Result : Unsatisfiable 0.64s 0.83s
% Output : Proof 1.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA126-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.15/0.33 % Computer : n001.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 22:27:50 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.64/0.83 % SZS status Unsatisfiable
% 0.64/0.83 % SZS output start Proof
% 0.64/0.83 tff(r_type, type, (
% 0.64/0.83 r: ( $i * $i ) > $o)).
% 0.64/0.83 tff(z_type, type, (
% 0.64/0.83 z: $i)).
% 0.64/0.83 tff(s_type, type, (
% 0.64/0.83 s: $i > $i)).
% 0.64/0.83 tff(b_type, type, (
% 0.64/0.83 b: ( $i * $i ) > $o)).
% 0.64/0.83 tff(elem_1_type, type, (
% 0.64/0.83 elem_1: $i)).
% 0.64/0.83 tff(inj_0_type, type, (
% 0.64/0.83 inj_0: $i > $i)).
% 0.64/0.83 tff(1,plain,
% 0.64/0.83 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(2,plain,
% 0.64/0.83 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(3,plain,
% 0.64/0.83 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.64/0.83 inference(rewrite,[status(thm)],[])).
% 0.64/0.83 tff(4,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','sinj')).
% 0.64/0.83 tff(5,plain,
% 0.64/0.83 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.64/0.83 tff(6,plain,(
% 0.64/0.83 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.64/0.83 inference(skolemize,[status(sab)],[5])).
% 0.64/0.83 tff(7,plain,
% 0.64/0.83 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.64/0.83 tff(8,plain,
% 0.64/0.83 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[7, 1])).
% 0.64/0.83 tff(9,plain,
% 0.64/0.83 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(10,plain,
% 0.64/0.83 (inj_0(s(elem!1)) = elem!1),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[9, 8])).
% 0.64/0.83 tff(11,assumption,(~(s(s(s(elem!1))) = s(elem!1))), introduced(assumption)).
% 0.64/0.83 tff(12,plain,
% 0.64/0.83 ((s(s(s(elem!1))) = s(elem!1)) <=> (s(elem!1) = s(s(s(elem!1))))),
% 0.64/0.83 inference(commutativity,[status(thm)],[])).
% 0.64/0.83 tff(13,plain,
% 0.64/0.83 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(elem!1))),
% 0.64/0.83 inference(symmetry,[status(thm)],[12])).
% 0.64/0.83 tff(14,assumption,(s(elem!1) = s(s(s(elem!1)))), introduced(assumption)).
% 0.64/0.83 tff(15,plain,
% 0.64/0.83 (s(s(s(elem!1))) = s(elem!1)),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.64/0.83 tff(16,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[11, 15])).
% 0.64/0.83 tff(17,plain,((~(s(elem!1) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(18,plain,
% 0.64/0.83 (~(s(elem!1) = s(s(s(elem!1))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[17, 11])).
% 0.64/0.83 tff(19,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 0.64/0.83 tff(20,plain,
% 0.64/0.83 (s(elem!1) = s(s(s(elem!1)))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[19])).
% 0.64/0.83 tff(21,assumption,(~(s(elem!1) = s(s(s(elem!1))))), introduced(assumption)).
% 0.64/0.83 tff(22,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[21, 20])).
% 0.64/0.83 tff(23,plain,((~(elem!1 = s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(24,plain,
% 0.64/0.83 (~(elem!1 = s(s(elem!1)))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[23, 18])).
% 0.64/0.83 tff(25,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 0.64/0.83 tff(26,plain,
% 0.64/0.83 (elem!1 = s(s(elem!1))),
% 0.64/0.83 inference(symmetry,[status(thm)],[25])).
% 0.64/0.83 tff(27,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 0.64/0.83 tff(28,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[27, 26])).
% 0.64/0.83 tff(29,plain,((~(s(s(elem!1)) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(30,plain,
% 0.64/0.83 (~(s(s(elem!1)) = elem!1)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[29, 24])).
% 0.64/0.83 tff(31,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 0.64/0.83 tff(32,plain,
% 0.64/0.83 (s(s(elem!1)) = s(elem!1)),
% 0.64/0.83 inference(monotonicity,[status(thm)],[31])).
% 0.64/0.83 tff(33,plain,
% 0.64/0.83 (s(elem!1) = s(s(elem!1))),
% 0.64/0.83 inference(symmetry,[status(thm)],[32])).
% 0.64/0.83 tff(34,plain,
% 0.64/0.83 (elem!1 = s(elem!1)),
% 0.64/0.83 inference(symmetry,[status(thm)],[31])).
% 0.64/0.83 tff(35,plain,
% 0.64/0.83 (elem!1 = s(s(elem!1))),
% 0.64/0.83 inference(transitivity,[status(thm)],[34, 33])).
% 0.64/0.83 tff(36,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[27, 35])).
% 0.64/0.83 tff(37,plain,((~(s(elem!1) = elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(38,plain,
% 0.64/0.83 (~(s(elem!1) = elem!1)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[37, 24])).
% 0.64/0.83 tff(39,plain,
% 0.64/0.83 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 0.64/0.83 inference(commutativity,[status(thm)],[])).
% 0.64/0.83 tff(40,plain,
% 0.64/0.83 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 0.64/0.83 inference(symmetry,[status(thm)],[39])).
% 0.64/0.83 tff(41,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 0.64/0.83 tff(42,plain,
% 0.64/0.83 (s(elem!1) = elem!1),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[41, 40])).
% 0.64/0.83 tff(43,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 0.64/0.83 tff(44,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[43, 42])).
% 0.64/0.83 tff(45,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(46,plain,
% 0.64/0.83 (~(elem!1 = s(elem!1))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[45, 38])).
% 0.64/0.83 tff(47,plain,
% 0.64/0.83 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(48,plain,
% 0.64/0.83 (inj_0(s(s(elem!1))) = s(elem!1)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[47, 8])).
% 0.64/0.83 tff(49,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 0.64/0.83 tff(50,plain,
% 0.64/0.83 (s(elem!1) = s(s(elem!1))),
% 0.64/0.83 inference(symmetry,[status(thm)],[49])).
% 0.64/0.83 tff(51,plain,
% 0.64/0.83 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[50])).
% 0.64/0.83 tff(52,plain,
% 0.64/0.83 (elem!1 = inj_0(s(elem!1))),
% 0.64/0.83 inference(symmetry,[status(thm)],[10])).
% 0.64/0.83 tff(53,plain,
% 0.64/0.83 (elem!1 = s(elem!1)),
% 0.64/0.83 inference(transitivity,[status(thm)],[52, 51, 48])).
% 0.64/0.83 tff(54,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 0.64/0.83 tff(55,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[54, 53])).
% 0.64/0.83 tff(56,plain,((~(s(s(elem!1)) = s(elem!1))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(57,plain,
% 0.64/0.83 (~(s(s(elem!1)) = s(elem!1))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[56, 46])).
% 0.64/0.83 tff(58,assumption,(~(s(s(s(elem!1))) = elem!1)), introduced(assumption)).
% 0.64/0.83 tff(59,assumption,(~(s(z) = s(elem!1))), introduced(assumption)).
% 0.64/0.83 tff(60,assumption,(r(s(s(s(elem!1))), z)), introduced(assumption)).
% 0.64/0.83 tff(61,assumption,(b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 0.64/0.83 tff(62,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 0.64/0.83 tff(63,plain,
% 0.64/0.83 ((s(s(s(s(s(elem!1))))) = elem!1) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 0.64/0.83 inference(commutativity,[status(thm)],[])).
% 0.64/0.83 tff(64,plain,
% 0.64/0.83 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.64/0.83 inference(symmetry,[status(thm)],[63])).
% 0.64/0.83 tff(65,assumption,(~(elem!1 = s(z))), introduced(assumption)).
% 0.64/0.83 tff(66,assumption,(s(s(s(elem!1))) = s(s(elem!1))), introduced(assumption)).
% 0.64/0.83 tff(67,plain,
% 0.64/0.83 (s(s(elem!1)) = s(s(s(elem!1)))),
% 0.64/0.83 inference(symmetry,[status(thm)],[66])).
% 0.64/0.83 tff(68,plain,
% 0.64/0.83 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[67])).
% 0.64/0.83 tff(69,plain,
% 0.64/0.83 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(elem!1)))),
% 0.64/0.83 inference(symmetry,[status(thm)],[68])).
% 0.64/0.83 tff(70,plain,
% 0.64/0.83 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(71,plain,
% 0.64/0.83 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[70, 8])).
% 0.64/0.83 tff(72,plain,
% 0.64/0.83 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.64/0.83 inference(symmetry,[status(thm)],[71])).
% 0.64/0.83 tff(73,plain,
% 0.64/0.83 (s(s(elem!1)) = s(elem!1)),
% 0.64/0.83 inference(transitivity,[status(thm)],[72, 69, 48])).
% 0.64/0.83 tff(74,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 0.64/0.83 tff(75,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[74, 73])).
% 0.64/0.83 tff(76,plain,((~(s(s(s(elem!1))) = s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(77,plain,
% 0.64/0.83 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[76, 57])).
% 0.64/0.83 tff(78,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 0.64/0.83 tff(79,plain,
% 0.64/0.83 (s(s(s(elem!1))) = s(s(elem!1))),
% 0.64/0.83 inference(symmetry,[status(thm)],[78])).
% 0.64/0.83 tff(80,assumption,(~(s(s(s(elem!1))) = s(s(elem!1)))), introduced(assumption)).
% 0.64/0.83 tff(81,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[80, 79])).
% 0.64/0.83 tff(82,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(83,plain,
% 0.64/0.83 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[82, 77])).
% 0.64/0.83 tff(84,plain,
% 0.64/0.83 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 0.64/0.83 inference(commutativity,[status(thm)],[])).
% 0.64/0.83 tff(85,plain,
% 0.64/0.83 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 0.64/0.83 inference(symmetry,[status(thm)],[84])).
% 0.64/0.83 tff(86,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 0.64/0.83 tff(87,plain,
% 0.64/0.83 (s(z) = s(elem!1)),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[86, 85])).
% 0.64/0.83 tff(88,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[59, 87])).
% 0.64/0.83 tff(89,plain,((~(s(elem!1) = s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(90,plain,
% 0.64/0.83 (~(s(elem!1) = s(z))),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[89, 59])).
% 0.64/0.83 tff(91,assumption,(~r(elem!1, s(z))), introduced(assumption)).
% 0.64/0.83 tff(92,plain,
% 0.64/0.83 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 0.64/0.83 inference(commutativity,[status(thm)],[])).
% 0.64/0.83 tff(93,plain,
% 0.64/0.83 ((~(elem!1 = s(z))) <=> (~(s(z) = elem!1))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[92])).
% 0.64/0.83 tff(94,plain,
% 0.64/0.83 (~(s(z) = elem!1)),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[65, 93])).
% 0.64/0.83 tff(95,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 0.64/0.83 tff(96,plain,
% 0.64/0.83 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 0.64/0.83 inference(symmetry,[status(thm)],[92])).
% 0.64/0.83 tff(97,assumption,(s(z) = s(elem!1)), introduced(assumption)).
% 0.64/0.83 tff(98,plain,
% 0.64/0.83 (s(elem!1) = s(z)),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[97, 84])).
% 0.64/0.83 tff(99,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 0.64/0.83 tff(100,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[99, 98])).
% 0.64/0.83 tff(101,plain,((~(s(z) = s(elem!1))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(102,plain,
% 0.64/0.83 (s(elem!1) = s(z)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[101, 97])).
% 0.64/0.83 tff(103,plain,
% 0.64/0.83 (s(z) = s(elem!1)),
% 0.64/0.83 inference(symmetry,[status(thm)],[86])).
% 0.64/0.83 tff(104,plain,
% 0.64/0.83 (inj_0(s(z)) = inj_0(s(elem!1))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[103])).
% 0.64/0.83 tff(105,plain,
% 0.64/0.83 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 0.64/0.83 inference(quant_inst,[status(thm)],[])).
% 0.64/0.83 tff(106,plain,
% 0.64/0.83 (inj_0(s(z)) = z),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[105, 8])).
% 0.64/0.83 tff(107,plain,
% 0.64/0.83 (z = inj_0(s(z))),
% 0.64/0.83 inference(symmetry,[status(thm)],[106])).
% 0.64/0.83 tff(108,plain,
% 0.64/0.83 (z = elem!1),
% 0.64/0.83 inference(transitivity,[status(thm)],[107, 104, 10])).
% 0.64/0.83 tff(109,assumption,(~(z = elem!1)), introduced(assumption)).
% 0.64/0.83 tff(110,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[109, 108])).
% 0.64/0.83 tff(111,plain,((~(s(elem!1) = s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(112,plain,
% 0.64/0.83 (z = elem!1),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[111, 102])).
% 0.64/0.83 tff(113,plain,
% 0.64/0.83 (b(s(z), elem!1) <=> b(s(elem!1), elem!1)),
% 0.64/0.83 inference(monotonicity,[status(thm)],[97])).
% 0.64/0.83 tff(114,plain,
% 0.64/0.83 (b(s(elem!1), elem!1) <=> b(s(z), elem!1)),
% 0.64/0.83 inference(symmetry,[status(thm)],[113])).
% 0.64/0.83 tff(115,plain,
% 0.64/0.83 ((~b(s(elem!1), elem!1)) <=> (~b(s(z), elem!1))),
% 0.64/0.83 inference(monotonicity,[status(thm)],[114])).
% 0.64/0.83 tff(116,plain,
% 0.64/0.83 (~b(s(z), elem!1)),
% 0.64/0.83 inference(modus_ponens,[status(thm)],[62, 115])).
% 0.64/0.83 tff(117,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 0.64/0.83 tff(118,plain,
% 0.64/0.83 ($false),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[117, 116])).
% 0.64/0.83 tff(119,plain,((~(s(z) = s(elem!1))) | (~b(s(z), elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.83 tff(120,plain,
% 0.64/0.83 (~b(s(z), elem!1)),
% 0.64/0.83 inference(unit_resolution,[status(thm)],[119, 97, 62])).
% 0.64/0.83 tff(121,assumption,(elem!1 = z), introduced(assumption)).
% 0.64/0.83 tff(122,plain,
% 0.64/0.83 (s(elem!1) = s(z)),
% 0.64/0.83 inference(monotonicity,[status(thm)],[121])).
% 0.64/0.83 tff(123,plain,
% 0.64/0.83 (s(z) = s(elem!1)),
% 0.64/0.83 inference(symmetry,[status(thm)],[122])).
% 0.64/0.83 tff(124,plain,
% 0.64/0.83 (b(s(z), elem!1) <=> b(s(elem!1), z)),
% 0.64/0.83 inference(monotonicity,[status(thm)],[123, 121])).
% 0.64/0.83 tff(125,plain,
% 0.64/0.83 (b(s(elem!1), z) <=> b(s(z), elem!1)),
% 0.64/0.84 inference(symmetry,[status(thm)],[124])).
% 0.64/0.84 tff(126,plain,
% 0.64/0.84 (b(s(z), elem!1)),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[95, 125])).
% 0.64/0.84 tff(127,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 0.64/0.84 tff(128,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[127, 126])).
% 0.64/0.84 tff(129,plain,((~(elem!1 = z)) | b(s(z), elem!1) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(130,plain,
% 0.64/0.84 (~(elem!1 = z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[129, 120, 95])).
% 0.64/0.84 tff(131,plain,
% 0.64/0.84 ((elem!1 = z) <=> (z = elem!1)),
% 0.64/0.84 inference(commutativity,[status(thm)],[])).
% 0.64/0.84 tff(132,plain,
% 0.64/0.84 ((z = elem!1) <=> (elem!1 = z)),
% 0.64/0.84 inference(symmetry,[status(thm)],[131])).
% 0.64/0.84 tff(133,assumption,(z = elem!1), introduced(assumption)).
% 0.64/0.84 tff(134,plain,
% 0.64/0.84 (elem!1 = z),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[133, 132])).
% 0.64/0.84 tff(135,assumption,(~(elem!1 = z)), introduced(assumption)).
% 0.64/0.84 tff(136,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[135, 134])).
% 0.64/0.84 tff(137,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(138,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[137, 130, 112])).
% 0.64/0.84 tff(139,plain,((~(s(z) = s(elem!1))) | (~b(s(elem!1), z)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(140,plain,
% 0.64/0.84 (~(s(z) = s(elem!1))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[139, 95, 62])).
% 0.64/0.84 tff(141,plain,
% 0.64/0.84 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.64/0.84 inference(bind,[status(th)],[])).
% 0.64/0.84 tff(142,plain,
% 0.64/0.84 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.84 inference(quant_intro,[status(thm)],[141])).
% 0.64/0.84 tff(143,plain,
% 0.64/0.84 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(144,plain,
% 0.64/0.84 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.64/0.84 inference(bind,[status(th)],[])).
% 0.64/0.84 tff(145,plain,
% 0.64/0.84 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.84 inference(quant_intro,[status(thm)],[144])).
% 0.64/0.84 tff(146,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rb')).
% 0.64/0.84 tff(147,plain,
% 0.64/0.84 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[146, 145])).
% 0.64/0.84 tff(148,plain,
% 0.64/0.84 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[147, 143])).
% 0.64/0.84 tff(149,plain,(
% 0.64/0.84 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.84 inference(skolemize,[status(sab)],[148])).
% 0.64/0.84 tff(150,plain,
% 0.64/0.84 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[149, 142])).
% 0.64/0.84 tff(151,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(152,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z)))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(153,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[152, 151])).
% 0.64/0.84 tff(154,plain,
% 0.64/0.84 ((elem!1 = s(z)) | b(elem!1, s(z)) | r(elem!1, s(z))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[153, 150])).
% 0.64/0.84 tff(155,plain,
% 0.64/0.84 (b(elem!1, s(z))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[154, 65, 91])).
% 0.64/0.84 tff(156,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 0.64/0.84 tff(157,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 0.64/0.84 tff(158,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 0.64/0.84 tff(159,assumption,(elem!1 = s(z)), introduced(assumption)).
% 0.64/0.84 tff(160,plain,
% 0.64/0.84 (s(z) = elem!1),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[159, 92])).
% 0.64/0.84 tff(161,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[156, 160])).
% 0.64/0.84 tff(162,plain,((~(elem!1 = s(z))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(163,plain,
% 0.64/0.84 (~(elem!1 = s(z))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[162, 156])).
% 0.64/0.84 tff(164,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(165,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(166,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[165, 164])).
% 0.64/0.84 tff(167,plain,
% 0.64/0.84 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[166, 150])).
% 0.64/0.84 tff(168,plain,
% 0.64/0.84 (r(s(elem!1), elem!1)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[167, 62, 38])).
% 0.64/0.84 tff(169,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 0.64/0.84 tff(170,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 0.64/0.84 tff(171,plain,
% 0.64/0.84 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))))),
% 0.64/0.84 inference(bind,[status(th)],[])).
% 0.64/0.84 tff(172,plain,
% 0.64/0.84 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.64/0.84 inference(quant_intro,[status(thm)],[171])).
% 0.64/0.84 tff(173,plain,
% 0.64/0.84 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(174,plain,
% 0.64/0.84 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~r(X0, X1)) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X1)))), ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) <=> (((~r(X1, X2)) | (~r(X0, X1))) | (~r(X0, X3))))), rewrite((((~r(X1, X2)) | (~r(X0, X1))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))), ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) <=> ((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))))), (((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> (((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) | (~r(X1, X3))))), rewrite((((~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))), (((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))))),
% 0.64/0.84 inference(bind,[status(th)],[])).
% 0.64/0.84 tff(175,plain,
% 0.64/0.84 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.64/0.84 inference(quant_intro,[status(thm)],[174])).
% 0.64/0.84 tff(176,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~r(X0, X1)) | (~r(X1, X2))) | (~r(X0, X3))) | (~r(X1, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axr')).
% 0.64/0.84 tff(177,plain,
% 0.64/0.84 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[176, 175])).
% 0.64/0.84 tff(178,plain,
% 0.64/0.84 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[177, 173])).
% 0.64/0.84 tff(179,plain,(
% 0.64/0.84 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.64/0.84 inference(skolemize,[status(sab)],[178])).
% 0.64/0.84 tff(180,plain,
% 0.64/0.84 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[179, 172])).
% 0.64/0.84 tff(181,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(182,plain,
% 0.64/0.84 (((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(183,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[182])).
% 0.64/0.84 tff(184,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1)))),
% 0.64/0.84 inference(transitivity,[status(thm)],[183, 181])).
% 0.64/0.84 tff(185,plain,
% 0.64/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(186,plain,
% 0.64/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))) | (~r(s(z), elem!1))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[185, 184])).
% 0.64/0.84 tff(187,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[186, 180, 170, 169, 158])).
% 0.64/0.84 tff(188,plain,((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(189,plain,
% 0.64/0.84 (~r(s(z), elem!1)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[188, 158, 168])).
% 0.64/0.84 tff(190,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(191,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(192,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.64/0.84 tff(193,plain,
% 0.64/0.84 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[192, 150])).
% 0.64/0.84 tff(194,plain,
% 0.64/0.84 (b(s(z), elem!1)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[193, 189, 156])).
% 0.64/0.84 tff(195,assumption,(b(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.64/0.84 tff(196,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 0.64/0.84 tff(197,plain,
% 0.64/0.84 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))),
% 0.64/0.84 inference(bind,[status(th)],[])).
% 0.64/0.84 tff(198,plain,
% 0.64/0.84 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(quant_intro,[status(thm)],[197])).
% 0.64/0.84 tff(199,plain,
% 0.64/0.84 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(200,plain,
% 0.64/0.84 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~b(X0, X1)) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> (((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> (((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))))), rewrite((((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))))),
% 0.64/0.84 inference(bind,[status(th)],[])).
% 0.64/0.84 tff(201,plain,
% 0.64/0.84 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(quant_intro,[status(thm)],[200])).
% 0.64/0.84 tff(202,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','axb')).
% 0.64/0.84 tff(203,plain,
% 0.64/0.84 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.64/0.84 tff(204,plain,
% 0.64/0.84 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[203, 199])).
% 0.64/0.84 tff(205,plain,(
% 0.64/0.84 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(skolemize,[status(sab)],[204])).
% 0.64/0.84 tff(206,plain,
% 0.64/0.84 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[205, 198])).
% 0.64/0.84 tff(207,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(208,plain,
% 0.64/0.84 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(209,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[208])).
% 0.64/0.84 tff(210,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[209, 207])).
% 0.64/0.84 tff(211,plain,
% 0.64/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(212,plain,
% 0.64/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[211, 210])).
% 0.64/0.84 tff(213,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[212, 206, 95, 195, 196])).
% 0.64/0.84 tff(214,plain,((~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(215,plain,
% 0.64/0.84 (~b(s(s(elem!1)), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[214, 195, 95])).
% 0.64/0.84 tff(216,plain,
% 0.64/0.84 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 0.64/0.84 inference(bind,[status(th)],[])).
% 0.64/0.84 tff(217,plain,
% 0.64/0.84 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.64/0.84 inference(quant_intro,[status(thm)],[216])).
% 0.64/0.84 tff(218,plain,
% 0.64/0.84 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(219,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','snz')).
% 0.64/0.84 tff(220,plain,
% 0.64/0.84 (![X: $i] : (~(s(X) = z))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[219, 218])).
% 0.64/0.84 tff(221,plain,(
% 0.64/0.84 ![X: $i] : (~(s(X) = z))),
% 0.64/0.84 inference(skolemize,[status(sab)],[220])).
% 0.64/0.84 tff(222,plain,
% 0.64/0.84 (![X: $i] : (~(s(X) = z))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.64/0.84 tff(223,plain,
% 0.64/0.84 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(224,plain,
% 0.64/0.84 (~(s(s(elem!1)) = z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[223, 222])).
% 0.64/0.84 tff(225,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(226,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(227,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = z) | b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.64/0.84 tff(228,plain,
% 0.64/0.84 (b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[227, 150, 224])).
% 0.64/0.84 tff(229,plain,
% 0.64/0.84 (r(s(s(elem!1)), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[228, 215])).
% 0.64/0.84 tff(230,assumption,(z = s(elem!1)), introduced(assumption)).
% 0.64/0.84 tff(231,plain,
% 0.64/0.84 (s(elem!1) = z),
% 0.64/0.84 inference(symmetry,[status(thm)],[230])).
% 0.64/0.84 tff(232,plain,
% 0.64/0.84 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(233,plain,
% 0.64/0.84 (~(s(elem!1) = z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[232, 222])).
% 0.64/0.84 tff(234,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[233, 231])).
% 0.64/0.84 tff(235,plain,(~(z = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(236,plain,
% 0.64/0.84 (s(z) = s(elem!1)),
% 0.64/0.84 inference(monotonicity,[status(thm)],[133])).
% 0.64/0.84 tff(237,plain,
% 0.64/0.84 (s(elem!1) = s(z)),
% 0.64/0.84 inference(symmetry,[status(thm)],[236])).
% 0.64/0.84 tff(238,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[99, 237])).
% 0.64/0.84 tff(239,plain,((~(z = elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(240,plain,
% 0.64/0.84 (~(z = elem!1)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[239, 99])).
% 0.64/0.84 tff(241,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 0.64/0.84 tff(242,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.64/0.84 tff(243,assumption,(r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 0.64/0.84 tff(244,plain,
% 0.64/0.84 (~(s(z) = s(elem!1))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[101, 99])).
% 0.64/0.84 tff(245,plain,
% 0.64/0.84 ((s(s(elem!1)) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(elem!1)))),
% 0.64/0.84 inference(commutativity,[status(thm)],[])).
% 0.64/0.84 tff(246,plain,
% 0.64/0.84 ((s(s(s(elem!1))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(elem!1))))),
% 0.64/0.84 inference(symmetry,[status(thm)],[245])).
% 0.64/0.84 tff(247,plain,
% 0.64/0.84 ((~(s(s(s(elem!1))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(elem!1)))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[246])).
% 0.64/0.84 tff(248,plain,
% 0.64/0.84 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[77, 247])).
% 0.64/0.84 tff(249,plain,
% 0.64/0.84 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 0.64/0.84 inference(commutativity,[status(thm)],[])).
% 0.64/0.84 tff(250,plain,
% 0.64/0.84 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 0.64/0.84 inference(symmetry,[status(thm)],[249])).
% 0.64/0.84 tff(251,plain,
% 0.64/0.84 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[250])).
% 0.64/0.84 tff(252,plain,
% 0.64/0.84 (~(s(s(elem!1)) = elem!1)),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[24, 251])).
% 0.64/0.84 tff(253,plain,
% 0.64/0.84 (r(s(elem!1), elem!1)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[167, 38, 62])).
% 0.64/0.84 tff(254,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.64/0.84 tff(255,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.64/0.84 tff(256,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(257,plain,
% 0.64/0.84 (((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(258,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[257])).
% 0.64/0.84 tff(259,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 0.64/0.84 inference(transitivity,[status(thm)],[258, 256])).
% 0.64/0.84 tff(260,plain,
% 0.64/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(261,plain,
% 0.64/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[260, 259])).
% 0.64/0.84 tff(262,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[261, 180, 170, 254, 255])).
% 0.64/0.84 tff(263,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(264,plain,
% 0.64/0.84 (~r(s(s(elem!1)), elem!1)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[263, 254, 253])).
% 0.64/0.84 tff(265,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(266,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(267,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[266, 265])).
% 0.64/0.84 tff(268,plain,
% 0.64/0.84 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[267, 150, 264])).
% 0.64/0.84 tff(269,plain,
% 0.64/0.84 (b(s(s(elem!1)), elem!1)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[268, 252])).
% 0.64/0.84 tff(270,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 0.64/0.84 tff(271,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(272,plain,
% 0.64/0.84 (((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(273,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))))),
% 0.64/0.84 inference(monotonicity,[status(thm)],[272])).
% 0.64/0.84 tff(274,plain,
% 0.64/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.64/0.84 inference(transitivity,[status(thm)],[273, 271])).
% 0.64/0.84 tff(275,plain,
% 0.64/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(276,plain,
% 0.64/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.64/0.84 tff(277,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[276, 180, 270, 254, 241])).
% 0.64/0.84 tff(278,plain,((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(279,plain,
% 0.64/0.84 (~r(s(elem!1), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[278, 254, 241])).
% 0.64/0.84 tff(280,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(281,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(282,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = z) | b(s(elem!1), z) | r(s(elem!1), z)),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[281, 280])).
% 0.64/0.84 tff(283,plain,
% 0.64/0.84 (b(s(elem!1), z) | r(s(elem!1), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[282, 150, 233])).
% 0.64/0.84 tff(284,plain,
% 0.64/0.84 (b(s(elem!1), z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[283, 279])).
% 0.64/0.84 tff(285,plain,
% 0.64/0.84 (z = elem!1),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[121, 131])).
% 0.64/0.84 tff(286,plain,
% 0.64/0.84 ($false),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[109, 285])).
% 0.64/0.84 tff(287,plain,((~(elem!1 = z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.84 tff(288,plain,
% 0.64/0.84 (~(elem!1 = z)),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[287, 109])).
% 0.64/0.84 tff(289,assumption,(~b(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 0.64/0.84 tff(290,plain,
% 0.64/0.84 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 0.64/0.84 inference(rewrite,[status(thm)],[])).
% 0.64/0.84 tff(291,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1)))),
% 0.64/0.84 inference(quant_inst,[status(thm)],[])).
% 0.64/0.84 tff(292,plain,
% 0.64/0.84 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 0.64/0.84 inference(modus_ponens,[status(thm)],[291, 290])).
% 0.64/0.84 tff(293,plain,
% 0.64/0.84 ((s(s(s(elem!1))) = s(elem!1)) | b(s(s(s(elem!1))), s(elem!1)) | r(s(s(s(elem!1))), s(elem!1))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[292, 150])).
% 0.64/0.84 tff(294,plain,
% 0.64/0.84 (r(s(s(s(elem!1))), s(elem!1))),
% 0.64/0.84 inference(unit_resolution,[status(thm)],[293, 289, 11])).
% 0.64/0.85 tff(295,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(296,plain,
% 0.64/0.85 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(297,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[296])).
% 0.64/0.85 tff(298,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[297, 295])).
% 0.64/0.85 tff(299,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(300,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[299, 298])).
% 0.64/0.85 tff(301,plain,
% 0.64/0.85 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[300, 180, 294, 254])).
% 0.64/0.85 tff(302,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 0.64/0.85 tff(303,plain,
% 0.64/0.85 (r(s(s(s(elem!1))), s(elem!1))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[293, 11, 289])).
% 0.64/0.85 tff(304,assumption,(r(s(s(s(elem!1))), s(elem!1))), introduced(assumption)).
% 0.64/0.85 tff(305,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(306,plain,
% 0.64/0.85 (((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(307,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[306])).
% 0.64/0.85 tff(308,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.85 inference(transitivity,[status(thm)],[307, 305])).
% 0.64/0.85 tff(309,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(310,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[309, 308])).
% 0.64/0.85 tff(311,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[310, 180, 170, 302, 304])).
% 0.64/0.85 tff(312,plain,((~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(313,plain,
% 0.64/0.85 (~r(s(elem!1), elem!1)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[312, 303, 302])).
% 0.64/0.85 tff(314,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[167, 38, 313, 62])).
% 0.64/0.85 tff(315,plain,((s(s(s(elem!1))) = s(elem!1)) | b(s(elem!1), elem!1) | (~r(s(s(s(elem!1))), elem!1)) | b(s(s(s(elem!1))), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(316,plain,
% 0.64/0.85 (~r(s(s(s(elem!1))), elem!1)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[315, 289, 62, 11])).
% 0.64/0.85 tff(317,plain,
% 0.64/0.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(318,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(319,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[318, 317])).
% 0.64/0.85 tff(320,plain,
% 0.64/0.85 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[319, 150])).
% 0.64/0.85 tff(321,plain,
% 0.64/0.85 (b(s(s(s(elem!1))), elem!1)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[320, 316, 58])).
% 0.64/0.85 tff(322,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(323,plain,
% 0.64/0.85 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(324,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[323])).
% 0.64/0.85 tff(325,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[324, 322])).
% 0.64/0.85 tff(326,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(327,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[326, 325])).
% 0.64/0.85 tff(328,plain,
% 0.64/0.85 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[327, 206, 321, 269])).
% 0.64/0.85 tff(329,plain,
% 0.64/0.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(330,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(331,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(elem!1))) | b(s(s(s(elem!1))), s(s(elem!1))) | r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.64/0.85 tff(332,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[331, 150, 77, 328, 301])).
% 0.64/0.85 tff(333,plain,(b(s(s(s(elem!1))), s(elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(s(elem!1))) = elem!1) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(334,plain,
% 0.64/0.85 (b(s(s(s(elem!1))), s(elem!1))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[333, 254, 58, 62, 11])).
% 0.64/0.85 tff(335,assumption,(b(elem!1, s(elem!1))), introduced(assumption)).
% 0.64/0.85 tff(336,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(337,plain,
% 0.64/0.85 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(338,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[337])).
% 0.64/0.85 tff(339,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[338, 336])).
% 0.64/0.85 tff(340,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(341,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.64/0.85 tff(342,plain,
% 0.64/0.85 (~b(s(s(s(elem!1))), elem!1)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[341, 206, 335, 61])).
% 0.64/0.85 tff(343,plain,
% 0.64/0.85 (r(s(s(s(elem!1))), elem!1)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[320, 342, 58])).
% 0.64/0.85 tff(344,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(345,plain,
% 0.64/0.85 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1)))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(346,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[345])).
% 0.64/0.85 tff(347,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.85 inference(transitivity,[status(thm)],[346, 344])).
% 0.64/0.85 tff(348,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(349,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[348, 347])).
% 0.64/0.85 tff(350,plain,
% 0.64/0.85 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[349, 180, 170, 343])).
% 0.64/0.85 tff(351,plain,
% 0.64/0.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(352,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1)))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(353,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[352, 351])).
% 0.64/0.85 tff(354,plain,
% 0.64/0.85 ((s(elem!1) = s(s(s(elem!1)))) | b(s(elem!1), s(s(s(elem!1)))) | r(s(elem!1), s(s(s(elem!1))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[353, 150])).
% 0.64/0.85 tff(355,plain,
% 0.64/0.85 (b(s(elem!1), s(s(s(elem!1))))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[354, 350, 21])).
% 0.64/0.85 tff(356,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.64/0.85 tff(357,assumption,(b(s(s(s(elem!1))), z)), introduced(assumption)).
% 0.64/0.85 tff(358,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(359,plain,
% 0.64/0.85 (((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(360,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[359])).
% 0.64/0.85 tff(361,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 0.64/0.85 inference(transitivity,[status(thm)],[360, 358])).
% 0.64/0.85 tff(362,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(363,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[362, 361])).
% 0.64/0.85 tff(364,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[363, 206, 357, 95, 356])).
% 0.64/0.85 tff(365,plain,((~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(366,plain,
% 0.64/0.85 (~b(s(s(s(elem!1))), z)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[365, 355, 95])).
% 0.64/0.85 tff(367,plain,
% 0.64/0.85 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(368,plain,
% 0.64/0.85 (~(s(s(s(elem!1))) = z)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[367, 222])).
% 0.64/0.85 tff(369,plain,
% 0.64/0.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(370,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(371,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = z) | b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[370, 369])).
% 0.64/0.85 tff(372,plain,
% 0.64/0.85 (b(s(s(s(elem!1))), z) | r(s(s(s(elem!1))), z)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[371, 150, 368])).
% 0.64/0.85 tff(373,plain,
% 0.64/0.85 (r(s(s(s(elem!1))), z)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[372, 366])).
% 0.64/0.85 tff(374,assumption,(r(elem!1, z)), introduced(assumption)).
% 0.64/0.85 tff(375,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(376,plain,
% 0.64/0.85 (((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(377,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[376])).
% 0.64/0.85 tff(378,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.85 inference(transitivity,[status(thm)],[377, 375])).
% 0.64/0.85 tff(379,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(380,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[379, 378])).
% 0.64/0.85 tff(381,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[380, 180, 302, 374, 60])).
% 0.64/0.85 tff(382,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(383,plain,
% 0.64/0.85 (~r(elem!1, z)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[382, 373, 343])).
% 0.64/0.85 tff(384,plain,
% 0.64/0.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(385,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(386,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.64/0.85 tff(387,plain,
% 0.64/0.85 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[386, 150])).
% 0.64/0.85 tff(388,plain,
% 0.64/0.85 (b(elem!1, z)),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[387, 383, 135])).
% 0.64/0.85 tff(389,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(390,plain,
% 0.64/0.85 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(391,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))))),
% 0.64/0.85 inference(monotonicity,[status(thm)],[390])).
% 0.64/0.85 tff(392,plain,
% 0.64/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 0.64/0.85 inference(transitivity,[status(thm)],[391, 389])).
% 0.64/0.85 tff(393,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(394,plain,
% 0.64/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.64/0.85 tff(395,plain,
% 0.64/0.85 ($false),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[394, 206, 335, 388, 95, 355])).
% 0.64/0.85 tff(396,plain,((~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (elem!1 = z) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.85 tff(397,plain,
% 0.64/0.85 (~b(elem!1, s(elem!1))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[396, 334, 288, 18, 253, 58, 284])).
% 0.64/0.85 tff(398,plain,
% 0.64/0.85 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 0.64/0.85 inference(rewrite,[status(thm)],[])).
% 0.64/0.85 tff(399,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1)))),
% 0.64/0.85 inference(quant_inst,[status(thm)],[])).
% 0.64/0.85 tff(400,plain,
% 0.64/0.85 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 0.64/0.85 inference(modus_ponens,[status(thm)],[399, 398])).
% 0.64/0.85 tff(401,plain,
% 0.64/0.85 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[400, 150])).
% 0.64/0.85 tff(402,plain,
% 0.64/0.85 (r(elem!1, s(elem!1))),
% 0.64/0.85 inference(unit_resolution,[status(thm)],[401, 397, 46])).
% 0.64/0.85 tff(403,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(404,plain,
% 0.64/0.86 (((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(405,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[404])).
% 0.64/0.86 tff(406,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[405, 403])).
% 0.64/0.86 tff(407,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(408,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[407, 406])).
% 0.64/0.86 tff(409,plain,
% 0.64/0.86 (~r(elem!1, s(s(elem!1)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[408, 180, 402, 254])).
% 0.64/0.86 tff(410,plain,
% 0.64/0.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(411,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(412,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[411, 410])).
% 0.64/0.86 tff(413,plain,
% 0.64/0.86 (b(elem!1, s(s(elem!1)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[412, 150, 24, 409])).
% 0.64/0.86 tff(414,plain,
% 0.64/0.86 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = elem!1)),
% 0.64/0.86 inference(commutativity,[status(thm)],[])).
% 0.64/0.86 tff(415,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 0.64/0.86 tff(416,plain,
% 0.64/0.86 (s(s(s(elem!1))) = elem!1),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.64/0.86 tff(417,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[58, 416])).
% 0.64/0.86 tff(418,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(419,plain,
% 0.64/0.86 (~(elem!1 = s(s(s(elem!1))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[418, 58])).
% 0.64/0.86 tff(420,plain,
% 0.64/0.86 ((s(z) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(z))),
% 0.64/0.86 inference(commutativity,[status(thm)],[])).
% 0.64/0.86 tff(421,plain,
% 0.64/0.86 ((s(s(s(elem!1))) = s(z)) <=> (s(z) = s(s(s(elem!1))))),
% 0.64/0.86 inference(symmetry,[status(thm)],[420])).
% 0.64/0.86 tff(422,plain,
% 0.64/0.86 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(z) = s(s(s(elem!1)))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[421])).
% 0.64/0.86 tff(423,assumption,(s(s(s(elem!1))) = s(z)), introduced(assumption)).
% 0.64/0.86 tff(424,plain,
% 0.64/0.86 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[423])).
% 0.64/0.86 tff(425,plain,
% 0.64/0.86 (s(s(elem!1)) = z),
% 0.64/0.86 inference(transitivity,[status(thm)],[72, 424, 106])).
% 0.64/0.86 tff(426,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[224, 425])).
% 0.64/0.86 tff(427,plain,(~(s(s(s(elem!1))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(428,plain,
% 0.64/0.86 (~(s(z) = s(s(s(elem!1))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[427, 422])).
% 0.64/0.86 tff(429,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(elem!1))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(430,plain,
% 0.64/0.86 (((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(z)))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(elem!1))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(431,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(elem!1)))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[430])).
% 0.64/0.86 tff(432,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(elem!1))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[431, 429])).
% 0.64/0.86 tff(433,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(434,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~r(s(z), s(elem!1)))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[433, 432])).
% 0.64/0.86 tff(435,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[434, 180, 304, 158, 243])).
% 0.64/0.86 tff(436,plain,((~r(s(z), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(437,plain,
% 0.64/0.86 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[436, 158, 243])).
% 0.64/0.86 tff(438,plain,
% 0.64/0.86 (b(s(s(s(elem!1))), s(elem!1))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[293, 437, 11])).
% 0.64/0.86 tff(439,plain,
% 0.64/0.86 (~b(elem!1, s(elem!1))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[396, 438, 135, 18, 170, 58, 95])).
% 0.64/0.86 tff(440,plain,
% 0.64/0.86 (r(elem!1, s(elem!1))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[401, 439, 46])).
% 0.64/0.86 tff(441,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 0.64/0.86 tff(442,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 0.64/0.86 tff(443,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(444,plain,
% 0.64/0.86 (((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(445,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z)))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[444])).
% 0.64/0.86 tff(446,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[445, 443])).
% 0.64/0.86 tff(447,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(448,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(elem!1, s(z)))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[447, 446])).
% 0.64/0.86 tff(449,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[448, 180, 442, 441, 158])).
% 0.64/0.86 tff(450,plain,((~r(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(451,plain,
% 0.64/0.86 (~r(elem!1, s(z))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[450, 440, 158])).
% 0.64/0.86 tff(452,plain,
% 0.64/0.86 (b(elem!1, s(z))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[154, 451, 65])).
% 0.64/0.86 tff(453,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(454,plain,
% 0.64/0.86 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(455,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[454])).
% 0.64/0.86 tff(456,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[455, 453])).
% 0.64/0.86 tff(457,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(458,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[457, 456])).
% 0.64/0.86 tff(459,plain,
% 0.64/0.86 (~b(elem!1, s(s(elem!1)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[458, 206, 452, 242])).
% 0.64/0.86 tff(460,plain,
% 0.64/0.86 (~r(elem!1, s(s(elem!1)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[408, 180, 440, 254])).
% 0.64/0.86 tff(461,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[412, 150, 24, 460, 459])).
% 0.64/0.86 tff(462,plain,((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (elem!1 = s(z)) | (elem!1 = z) | (~r(s(elem!1), elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(463,plain,
% 0.64/0.86 (~r(s(z), s(elem!1))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[462, 254, 242, 65, 288, 253, 58, 284, 11, 243])).
% 0.64/0.86 tff(464,plain,
% 0.64/0.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(465,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1)))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(466,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[465, 464])).
% 0.64/0.86 tff(467,plain,
% 0.64/0.86 ((s(z) = s(elem!1)) | b(s(z), s(elem!1)) | r(s(z), s(elem!1))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[466, 150])).
% 0.64/0.86 tff(468,plain,
% 0.64/0.86 (b(s(z), s(elem!1))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[467, 463, 59])).
% 0.64/0.86 tff(469,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(470,plain,
% 0.64/0.86 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(471,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1)))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[470])).
% 0.64/0.86 tff(472,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[471, 469])).
% 0.64/0.86 tff(473,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(474,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(elem!1)))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.64/0.86 tff(475,plain,
% 0.64/0.86 (~b(s(z), s(s(s(elem!1))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[474, 206, 334, 468])).
% 0.64/0.86 tff(476,plain,
% 0.64/0.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(477,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1)))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(478,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[477, 476])).
% 0.64/0.86 tff(479,plain,
% 0.64/0.86 ((s(z) = s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[478, 150, 475])).
% 0.64/0.86 tff(480,plain,
% 0.64/0.86 (r(s(z), s(s(s(elem!1))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[479, 428])).
% 0.64/0.86 tff(481,plain,
% 0.64/0.86 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[349, 180, 170, 302])).
% 0.64/0.86 tff(482,plain,
% 0.64/0.86 (b(s(elem!1), s(s(s(elem!1))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[354, 481, 21])).
% 0.64/0.86 tff(483,plain,
% 0.64/0.86 (~b(s(s(s(elem!1))), z)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[365, 482, 284])).
% 0.64/0.86 tff(484,plain,
% 0.64/0.86 (r(s(s(s(elem!1))), z)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[372, 483])).
% 0.64/0.86 tff(485,assumption,(r(z, s(z))), introduced(assumption)).
% 0.64/0.86 tff(486,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(487,plain,
% 0.64/0.86 (((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(488,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[487])).
% 0.64/0.86 tff(489,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[488, 486])).
% 0.64/0.86 tff(490,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(elem!1))), z)))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(491,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z))) | (~r(z, s(z)))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[490, 489])).
% 0.64/0.86 tff(492,plain,
% 0.64/0.86 ($false),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[491, 180, 60, 485, 243])).
% 0.64/0.86 tff(493,plain,((~r(z, s(z))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.86 tff(494,plain,
% 0.64/0.86 (~r(z, s(z))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[493, 484, 243])).
% 0.64/0.86 tff(495,plain,
% 0.64/0.86 ((z = s(z)) <=> (s(z) = z)),
% 0.64/0.86 inference(commutativity,[status(thm)],[])).
% 0.64/0.86 tff(496,plain,
% 0.64/0.86 ((s(z) = z) <=> (z = s(z))),
% 0.64/0.86 inference(symmetry,[status(thm)],[495])).
% 0.64/0.86 tff(497,plain,
% 0.64/0.86 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[496])).
% 0.64/0.86 tff(498,plain,
% 0.64/0.86 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(499,plain,
% 0.64/0.86 (~(s(z) = z)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[498, 222])).
% 0.64/0.86 tff(500,plain,
% 0.64/0.86 (~(z = s(z))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[499, 497])).
% 0.64/0.86 tff(501,plain,
% 0.64/0.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(502,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(503,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[502, 501])).
% 0.64/0.86 tff(504,plain,
% 0.64/0.86 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[503, 150])).
% 0.64/0.86 tff(505,plain,
% 0.64/0.86 (b(z, s(z)) | r(z, s(z))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[504, 500])).
% 0.64/0.86 tff(506,plain,
% 0.64/0.86 (b(z, s(z))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[505, 494])).
% 0.64/0.86 tff(507,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 0.64/0.86 tff(508,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 0.64/0.86 tff(509,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.64/0.86 tff(510,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(511,plain,
% 0.64/0.86 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(512,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[511])).
% 0.64/0.86 tff(513,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[512, 510])).
% 0.64/0.86 tff(514,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(515,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.64/0.86 tff(516,plain,
% 0.64/0.86 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[515, 180, 484, 254, 241])).
% 0.64/0.86 tff(517,plain,
% 0.64/0.86 (~(elem!1 = s(s(elem!1)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[23, 21])).
% 0.64/0.86 tff(518,plain,
% 0.64/0.86 (~(s(elem!1) = elem!1)),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[37, 517])).
% 0.64/0.86 tff(519,plain,
% 0.64/0.86 (~(elem!1 = s(elem!1))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[45, 518])).
% 0.64/0.86 tff(520,plain,
% 0.64/0.86 (~(s(s(elem!1)) = s(elem!1))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[56, 519])).
% 0.64/0.86 tff(521,plain,
% 0.64/0.86 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[76, 520])).
% 0.64/0.86 tff(522,plain,
% 0.64/0.86 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[331, 150, 521, 516])).
% 0.64/0.86 tff(523,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(524,plain,
% 0.64/0.86 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(525,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.64/0.86 inference(monotonicity,[status(thm)],[524])).
% 0.64/0.86 tff(526,plain,
% 0.64/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.86 inference(transitivity,[status(thm)],[525, 523])).
% 0.64/0.86 tff(527,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(528,plain,
% 0.64/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[527, 526])).
% 0.64/0.86 tff(529,plain,
% 0.64/0.86 (~b(elem!1, s(s(s(elem!1))))),
% 0.64/0.86 inference(unit_resolution,[status(thm)],[528, 206, 522, 509])).
% 0.64/0.86 tff(530,plain,
% 0.64/0.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 0.64/0.86 inference(rewrite,[status(thm)],[])).
% 0.64/0.86 tff(531,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1)))))),
% 0.64/0.86 inference(quant_inst,[status(thm)],[])).
% 0.64/0.86 tff(532,plain,
% 0.64/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 0.64/0.86 inference(modus_ponens,[status(thm)],[531, 530])).
% 0.64/0.86 tff(533,plain,
% 0.64/0.86 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[532, 150])).
% 0.64/0.87 tff(534,plain,
% 0.64/0.87 (r(elem!1, s(s(s(elem!1))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[533, 529, 508])).
% 0.64/0.87 tff(535,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(536,plain,
% 0.64/0.87 (((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(537,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[536])).
% 0.64/0.87 tff(538,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[537, 535])).
% 0.64/0.87 tff(539,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(540,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(z)))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[539, 538])).
% 0.64/0.87 tff(541,plain,
% 0.64/0.87 (~r(elem!1, s(z))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[540, 180, 534, 507])).
% 0.64/0.87 tff(542,plain,
% 0.64/0.87 (b(elem!1, s(z))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[154, 541, 65])).
% 0.64/0.87 tff(543,assumption,(r(z, elem!1)), introduced(assumption)).
% 0.64/0.87 tff(544,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(545,plain,
% 0.64/0.87 (((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(546,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[545])).
% 0.64/0.87 tff(547,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.87 inference(transitivity,[status(thm)],[546, 544])).
% 0.64/0.87 tff(548,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(549,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.64/0.87 tff(550,plain,
% 0.64/0.87 ($false),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[549, 180, 543, 302, 60])).
% 0.64/0.87 tff(551,plain,((~r(s(s(s(elem!1))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(552,plain,
% 0.64/0.87 (~r(z, elem!1)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[551, 484, 302])).
% 0.64/0.87 tff(553,plain,
% 0.64/0.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(554,plain,
% 0.64/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(555,plain,
% 0.64/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.64/0.87 tff(556,plain,
% 0.64/0.87 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[555, 150])).
% 0.64/0.87 tff(557,plain,
% 0.64/0.87 (b(z, elem!1)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[556, 552, 109])).
% 0.64/0.87 tff(558,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(559,plain,
% 0.64/0.87 (((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(560,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[559])).
% 0.64/0.87 tff(561,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 0.64/0.87 inference(transitivity,[status(thm)],[560, 558])).
% 0.64/0.87 tff(562,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, elem!1)))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(563,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(z, elem!1))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.64/0.87 tff(564,plain,
% 0.64/0.87 ($false),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[563, 206, 557, 542, 506])).
% 0.64/0.87 tff(565,plain,((~r(s(s(s(elem!1))), elem!1)) | (elem!1 = s(z)) | (~r(s(z), s(s(s(elem!1))))) | (elem!1 = s(s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (z = elem!1) | (~r(s(s(s(elem!1))), s(z))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(566,plain,
% 0.64/0.87 (~r(s(s(s(elem!1))), elem!1)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[565, 480, 65, 419, 413, 254, 241, 109, 243, 18, 253])).
% 0.64/0.87 tff(567,plain,
% 0.64/0.87 (b(s(s(s(elem!1))), elem!1)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[320, 566, 58])).
% 0.64/0.87 tff(568,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(569,plain,
% 0.64/0.87 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(570,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[569])).
% 0.64/0.87 tff(571,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[570, 568])).
% 0.64/0.87 tff(572,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(573,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[572, 571])).
% 0.64/0.87 tff(574,plain,
% 0.64/0.87 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[573, 206, 567, 269])).
% 0.64/0.87 tff(575,plain,
% 0.64/0.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(576,plain,
% 0.64/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(577,plain,
% 0.64/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(elem!1)))) | b(s(s(elem!1)), s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[576, 575])).
% 0.64/0.87 tff(578,plain,
% 0.64/0.87 ((s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[577, 150, 574])).
% 0.64/0.87 tff(579,plain,
% 0.64/0.87 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[578, 248])).
% 0.64/0.87 tff(580,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 0.64/0.87 tff(581,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(582,plain,
% 0.64/0.87 (((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(583,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[582])).
% 0.64/0.87 tff(584,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[583, 581])).
% 0.64/0.87 tff(585,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(586,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.64/0.87 tff(587,plain,
% 0.64/0.87 ($false),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[586, 180, 60, 241, 580])).
% 0.64/0.87 tff(588,plain,((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(589,plain,
% 0.64/0.87 (~r(s(s(s(elem!1))), z)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[588, 579, 241])).
% 0.64/0.87 tff(590,plain,
% 0.64/0.87 (b(s(s(s(elem!1))), z)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[372, 589])).
% 0.64/0.87 tff(591,plain,
% 0.64/0.87 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[365, 590, 284])).
% 0.64/0.87 tff(592,plain,
% 0.64/0.87 (r(s(elem!1), s(s(s(elem!1))))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[354, 591, 18])).
% 0.64/0.87 tff(593,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(594,plain,
% 0.64/0.87 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(595,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[594])).
% 0.64/0.87 tff(596,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[595, 593])).
% 0.64/0.87 tff(597,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(598,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[597, 596])).
% 0.64/0.87 tff(599,plain,
% 0.64/0.87 ($false),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[598, 180, 592, 254, 579])).
% 0.64/0.87 tff(600,plain,((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), z)) | (s(s(s(elem!1))) = elem!1) | (elem!1 = s(z)) | (z = elem!1) | (~r(s(s(s(elem!1))), s(z))) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (s(z) = s(elem!1)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(601,plain,
% 0.64/0.87 (~r(s(s(elem!1)), s(elem!1))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[600, 240, 58, 65, 241, 243, 62, 11, 244, 242])).
% 0.64/0.87 tff(602,plain,
% 0.64/0.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(603,plain,
% 0.64/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1)))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(604,plain,
% 0.64/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[603, 602])).
% 0.64/0.87 tff(605,plain,
% 0.64/0.87 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[604, 150])).
% 0.64/0.87 tff(606,plain,
% 0.64/0.87 (b(s(s(elem!1)), s(elem!1))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[605, 601, 57])).
% 0.64/0.87 tff(607,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 0.64/0.87 tff(608,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(609,plain,
% 0.64/0.87 (((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(610,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1)))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[609])).
% 0.64/0.87 tff(611,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[610, 608])).
% 0.64/0.87 tff(612,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(z))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(613,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(z), s(elem!1)))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.64/0.87 tff(614,plain,
% 0.64/0.87 ($false),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[613, 206, 607, 195, 242])).
% 0.64/0.87 tff(615,plain,((~b(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.87 tff(616,plain,
% 0.64/0.87 (~b(s(z), s(elem!1))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[615, 606, 242])).
% 0.64/0.87 tff(617,plain,
% 0.64/0.87 (r(s(z), s(elem!1))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[467, 616, 244])).
% 0.64/0.87 tff(618,plain,
% 0.64/0.87 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[436, 617, 243])).
% 0.64/0.87 tff(619,plain,
% 0.64/0.87 (b(s(s(s(elem!1))), s(elem!1))),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[293, 618, 11])).
% 0.64/0.87 tff(620,plain,
% 0.64/0.87 (~(elem!1 = z)),
% 0.64/0.87 inference(unit_resolution,[status(thm)],[287, 240])).
% 0.64/0.87 tff(621,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(622,plain,
% 0.64/0.87 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(rewrite,[status(thm)],[])).
% 0.64/0.87 tff(623,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.64/0.87 inference(monotonicity,[status(thm)],[622])).
% 0.64/0.87 tff(624,plain,
% 0.64/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(transitivity,[status(thm)],[623, 621])).
% 0.64/0.87 tff(625,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.87 inference(quant_inst,[status(thm)],[])).
% 0.64/0.87 tff(626,plain,
% 0.64/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.64/0.87 inference(modus_ponens,[status(thm)],[625, 624])).
% 0.64/0.88 tff(627,plain,
% 0.64/0.88 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[626, 206, 619, 606])).
% 0.64/0.88 tff(628,plain,
% 0.64/0.88 ((s(s(elem!1)) = s(s(s(elem!1)))) | r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[577, 150, 627])).
% 0.64/0.88 tff(629,plain,
% 0.64/0.88 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[628, 248])).
% 0.64/0.88 tff(630,plain,
% 0.64/0.88 (~r(s(s(s(elem!1))), z)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[588, 629, 241])).
% 0.64/0.88 tff(631,plain,
% 0.64/0.88 (b(s(s(s(elem!1))), z)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[372, 630])).
% 0.64/0.88 tff(632,assumption,(b(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 0.64/0.88 tff(633,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(634,plain,
% 0.64/0.88 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(635,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[634])).
% 0.64/0.88 tff(636,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.88 inference(transitivity,[status(thm)],[635, 633])).
% 0.64/0.88 tff(637,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(638,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[637, 636])).
% 0.64/0.88 tff(639,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[638, 206, 61, 195, 632])).
% 0.64/0.88 tff(640,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(641,plain,
% 0.64/0.88 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[640, 619, 606])).
% 0.64/0.88 tff(642,plain,
% 0.64/0.88 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[331, 150, 77, 641])).
% 0.64/0.88 tff(643,assumption,(r(s(s(s(elem!1))), s(s(elem!1)))), introduced(assumption)).
% 0.64/0.88 tff(644,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(645,plain,
% 0.64/0.88 (((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(646,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[645])).
% 0.64/0.88 tff(647,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z)))),
% 0.64/0.88 inference(transitivity,[status(thm)],[646, 644])).
% 0.64/0.88 tff(648,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), elem!1)))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(649,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[648, 647])).
% 0.64/0.88 tff(650,plain,
% 0.64/0.88 ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(elem!1, z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[649, 180])).
% 0.64/0.88 tff(651,plain,
% 0.64/0.88 (~r(elem!1, z)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[650, 270, 170])).
% 0.64/0.88 tff(652,plain,
% 0.64/0.88 (b(elem!1, z)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[387, 651, 135])).
% 0.64/0.88 tff(653,assumption,(b(elem!1, z)), introduced(assumption)).
% 0.64/0.88 tff(654,assumption,(b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 0.64/0.88 tff(655,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(656,plain,
% 0.64/0.88 (((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(657,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[656])).
% 0.64/0.88 tff(658,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.64/0.88 inference(transitivity,[status(thm)],[657, 655])).
% 0.64/0.88 tff(659,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(660,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), elem!1))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[659, 658])).
% 0.64/0.88 tff(661,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[660, 206, 654, 653, 357])).
% 0.64/0.88 tff(662,plain,((~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(663,plain,
% 0.64/0.88 (~b(s(s(s(elem!1))), elem!1)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[662, 652, 357])).
% 0.64/0.88 tff(664,plain,
% 0.64/0.88 (r(s(s(s(elem!1))), elem!1)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[320, 663, 58])).
% 0.64/0.88 tff(665,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.64/0.88 tff(666,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(667,plain,
% 0.64/0.88 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(668,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[667])).
% 0.64/0.88 tff(669,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.88 inference(transitivity,[status(thm)],[668, 666])).
% 0.64/0.88 tff(670,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(671,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.64/0.88 tff(672,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[671, 180, 302, 643, 665])).
% 0.64/0.88 tff(673,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(674,plain,
% 0.64/0.88 (~r(elem!1, s(s(elem!1)))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[673, 664, 643])).
% 0.64/0.88 tff(675,plain,
% 0.64/0.88 (b(elem!1, s(s(elem!1)))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[412, 150, 517, 674])).
% 0.64/0.88 tff(676,plain,
% 0.64/0.88 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 0.64/0.88 inference(commutativity,[status(thm)],[])).
% 0.64/0.88 tff(677,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 0.64/0.88 tff(678,plain,
% 0.64/0.88 (s(s(elem!1)) = s(elem!1)),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[677, 676])).
% 0.64/0.88 tff(679,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[74, 678])).
% 0.64/0.88 tff(680,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(681,plain,
% 0.64/0.88 (~(s(elem!1) = s(s(elem!1)))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[680, 520])).
% 0.64/0.88 tff(682,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(683,plain,
% 0.64/0.88 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(684,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[683])).
% 0.64/0.88 tff(685,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 0.64/0.88 inference(transitivity,[status(thm)],[684, 682])).
% 0.64/0.88 tff(686,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(687,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[686, 685])).
% 0.64/0.88 tff(688,plain,
% 0.64/0.88 (~r(s(elem!1), s(s(elem!1)))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[687, 180, 270, 241])).
% 0.64/0.88 tff(689,plain,
% 0.64/0.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(690,plain,
% 0.64/0.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(691,plain,
% 0.64/0.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[690, 689])).
% 0.64/0.88 tff(692,plain,
% 0.64/0.88 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[691, 150])).
% 0.64/0.88 tff(693,plain,
% 0.64/0.88 (b(s(elem!1), s(s(elem!1)))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[692, 688, 681])).
% 0.64/0.88 tff(694,plain,
% 0.64/0.88 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[349, 180, 170, 664])).
% 0.64/0.88 tff(695,plain,
% 0.64/0.88 (b(s(elem!1), s(s(s(elem!1))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[354, 694, 21])).
% 0.64/0.88 tff(696,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(697,plain,
% 0.64/0.88 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(698,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[697])).
% 0.64/0.88 tff(699,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.88 inference(transitivity,[status(thm)],[698, 696])).
% 0.64/0.88 tff(700,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(701,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[700, 699])).
% 0.64/0.88 tff(702,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[701, 206, 157, 195, 242, 509])).
% 0.64/0.88 tff(703,plain,((~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(704,plain,
% 0.64/0.88 (~b(elem!1, s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[703, 675, 242, 195])).
% 0.64/0.88 tff(705,plain,
% 0.64/0.88 (r(elem!1, s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[154, 704, 65])).
% 0.64/0.88 tff(706,plain,
% 0.64/0.88 (~r(elem!1, s(elem!1))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[450, 705, 158])).
% 0.64/0.88 tff(707,plain,
% 0.64/0.88 (b(elem!1, s(elem!1))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[401, 706, 519])).
% 0.64/0.88 tff(708,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(709,plain,
% 0.64/0.88 (((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(710,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[709])).
% 0.64/0.88 tff(711,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.88 inference(transitivity,[status(thm)],[710, 708])).
% 0.64/0.88 tff(712,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(713,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1))))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[712, 711])).
% 0.64/0.88 tff(714,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[713, 206, 707, 695, 693, 675])).
% 0.64/0.88 tff(715,plain,((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (elem!1 = s(z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(elem!1))), z)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(716,plain,
% 0.64/0.88 (~r(s(elem!1), z)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[715, 617, 65, 242, 606, 18, 253, 241, 642, 58, 631, 620])).
% 0.64/0.88 tff(717,plain,
% 0.64/0.88 (b(s(elem!1), z)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[283, 716])).
% 0.64/0.88 tff(718,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(719,plain,
% 0.64/0.88 (((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(720,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[719])).
% 0.64/0.88 tff(721,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)))),
% 0.64/0.88 inference(transitivity,[status(thm)],[720, 718])).
% 0.64/0.88 tff(722,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(723,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (~b(s(elem!1), z))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[722, 721])).
% 0.64/0.88 tff(724,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[723, 206, 631, 717, 619])).
% 0.64/0.88 tff(725,plain,((s(elem!1) = s(z)) | (elem!1 = s(z)) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), s(z))) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(726,plain,
% 0.64/0.88 (~r(s(s(s(elem!1))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[725, 242, 58, 65, 99, 11, 62, 241])).
% 0.64/0.88 tff(727,assumption,(~r(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 0.64/0.88 tff(728,assumption,(~b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 0.64/0.88 tff(729,plain,
% 0.64/0.88 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(730,plain,
% 0.64/0.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z)))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(731,plain,
% 0.64/0.88 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(z)) | b(s(s(s(elem!1))), s(z)) | r(s(s(s(elem!1))), s(z))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[730, 729])).
% 0.64/0.88 tff(732,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[731, 150, 427, 728, 727])).
% 0.64/0.88 tff(733,plain,(r(s(s(s(elem!1))), s(z)) | b(s(s(s(elem!1))), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(734,plain,
% 0.64/0.88 (b(s(s(s(elem!1))), s(z))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[733, 726])).
% 0.64/0.88 tff(735,assumption,(b(s(s(s(elem!1))), s(z))), introduced(assumption)).
% 0.64/0.88 tff(736,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(737,plain,
% 0.64/0.88 (((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 0.64/0.88 inference(rewrite,[status(thm)],[])).
% 0.64/0.88 tff(738,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 0.64/0.88 inference(monotonicity,[status(thm)],[737])).
% 0.64/0.88 tff(739,plain,
% 0.64/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 0.64/0.88 inference(transitivity,[status(thm)],[738, 736])).
% 0.64/0.88 tff(740,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.64/0.88 inference(quant_inst,[status(thm)],[])).
% 0.64/0.88 tff(741,plain,
% 0.64/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 0.64/0.88 inference(modus_ponens,[status(thm)],[740, 739])).
% 0.64/0.88 tff(742,plain,
% 0.64/0.88 ($false),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[741, 206, 654, 157, 735])).
% 0.64/0.88 tff(743,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.88 tff(744,plain,
% 0.64/0.88 (~b(s(s(s(elem!1))), elem!1)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[743, 734, 157])).
% 0.64/0.88 tff(745,plain,
% 0.64/0.88 (r(s(s(s(elem!1))), elem!1)),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[320, 744, 58])).
% 0.64/0.88 tff(746,plain,
% 0.64/0.88 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.64/0.88 inference(unit_resolution,[status(thm)],[349, 180, 168, 745])).
% 0.64/0.89 tff(747,plain,
% 0.64/0.89 (b(s(elem!1), s(s(s(elem!1))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[354, 746, 18])).
% 0.64/0.89 tff(748,plain,
% 0.64/0.89 (~b(s(s(s(elem!1))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[365, 747, 95])).
% 0.64/0.89 tff(749,plain,
% 0.64/0.89 (r(s(s(s(elem!1))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[372, 748])).
% 0.64/0.89 tff(750,plain,
% 0.64/0.89 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[588, 749, 241])).
% 0.64/0.89 tff(751,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 0.64/0.89 tff(752,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(753,plain,
% 0.64/0.89 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(754,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[753])).
% 0.64/0.89 tff(755,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[754, 752])).
% 0.64/0.89 tff(756,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(757,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[756, 755])).
% 0.64/0.89 tff(758,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[757, 206, 735, 751, 242])).
% 0.64/0.89 tff(759,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(760,plain,
% 0.64/0.89 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[759, 734, 242])).
% 0.64/0.89 tff(761,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[577, 150, 760, 750, 83])).
% 0.64/0.89 tff(762,plain,((~b(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z))) | (elem!1 = s(z)) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(763,plain,
% 0.64/0.89 (~b(s(s(elem!1)), s(z))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[762, 229, 95, 58, 157, 65, 99, 11, 62])).
% 0.64/0.89 tff(764,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.64/0.89 tff(765,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 0.64/0.89 tff(766,plain,
% 0.64/0.89 (s(z) = s(s(elem!1))),
% 0.64/0.89 inference(symmetry,[status(thm)],[765])).
% 0.64/0.89 tff(767,plain,
% 0.64/0.89 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[766])).
% 0.64/0.89 tff(768,plain,
% 0.64/0.89 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 0.64/0.89 inference(symmetry,[status(thm)],[767])).
% 0.64/0.89 tff(769,plain,
% 0.64/0.89 (s(elem!1) = inj_0(s(s(elem!1)))),
% 0.64/0.89 inference(symmetry,[status(thm)],[48])).
% 0.64/0.89 tff(770,plain,
% 0.64/0.89 (s(elem!1) = z),
% 0.64/0.89 inference(transitivity,[status(thm)],[769, 768, 106])).
% 0.64/0.89 tff(771,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[233, 770])).
% 0.64/0.89 tff(772,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(773,assumption,(~r(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.64/0.89 tff(774,plain,
% 0.64/0.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(775,plain,
% 0.64/0.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z)))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(776,plain,
% 0.64/0.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[775, 774])).
% 0.64/0.89 tff(777,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[776, 150, 773, 772, 764])).
% 0.64/0.89 tff(778,plain,(b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(779,plain,
% 0.64/0.89 (r(s(s(elem!1)), s(z))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[778, 763])).
% 0.64/0.89 tff(780,assumption,(r(s(z), z)), introduced(assumption)).
% 0.64/0.89 tff(781,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.64/0.89 tff(782,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(783,plain,
% 0.64/0.89 (((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(784,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[783])).
% 0.64/0.89 tff(785,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 0.64/0.89 inference(transitivity,[status(thm)],[784, 782])).
% 0.64/0.89 tff(786,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(787,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[786, 785])).
% 0.64/0.89 tff(788,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[787, 180, 781, 780, 241])).
% 0.64/0.89 tff(789,plain,((~r(s(z), z)) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(790,plain,
% 0.64/0.89 (~r(s(z), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[789, 779, 229])).
% 0.64/0.89 tff(791,plain,
% 0.64/0.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(792,plain,
% 0.64/0.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(793,plain,
% 0.64/0.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[792, 791])).
% 0.64/0.89 tff(794,plain,
% 0.64/0.89 (b(s(z), z) | r(s(z), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[793, 150, 499])).
% 0.64/0.89 tff(795,plain,
% 0.64/0.89 (b(s(z), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[794, 790])).
% 0.64/0.89 tff(796,assumption,(b(s(z), z)), introduced(assumption)).
% 0.64/0.89 tff(797,assumption,(b(z, elem!1)), introduced(assumption)).
% 0.64/0.89 tff(798,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(799,plain,
% 0.64/0.89 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(800,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[799])).
% 0.64/0.89 tff(801,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1)))),
% 0.64/0.89 inference(transitivity,[status(thm)],[800, 798])).
% 0.64/0.89 tff(802,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(803,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), z)) | (~b(z, elem!1))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[802, 801])).
% 0.64/0.89 tff(804,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[803, 206, 117, 797, 796])).
% 0.64/0.89 tff(805,plain,((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(806,plain,
% 0.64/0.89 (~b(z, elem!1)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[805, 795, 117])).
% 0.64/0.89 tff(807,plain,
% 0.64/0.89 (r(z, elem!1)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[556, 806, 240])).
% 0.64/0.89 tff(808,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(809,plain,
% 0.64/0.89 (((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(810,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[809])).
% 0.64/0.89 tff(811,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[810, 808])).
% 0.64/0.89 tff(812,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, s(elem!1))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(813,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(z, s(elem!1)))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[812, 811])).
% 0.64/0.89 tff(814,plain,
% 0.64/0.89 (~r(z, s(elem!1))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[813, 180, 168, 807])).
% 0.64/0.89 tff(815,plain,
% 0.64/0.89 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(816,plain,
% 0.64/0.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1)))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(817,plain,
% 0.64/0.89 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(elem!1)) | b(z, s(elem!1)) | r(z, s(elem!1))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[816, 815])).
% 0.64/0.89 tff(818,plain,
% 0.64/0.89 (b(z, s(elem!1))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[817, 150, 814, 235])).
% 0.64/0.89 tff(819,plain,
% 0.64/0.89 (~b(s(s(s(elem!1))), elem!1)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[743, 735, 157])).
% 0.64/0.89 tff(820,plain,
% 0.64/0.89 (r(s(s(s(elem!1))), elem!1)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[320, 819, 58])).
% 0.64/0.89 tff(821,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(822,plain,
% 0.64/0.89 (((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(823,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[822])).
% 0.64/0.89 tff(824,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[823, 821])).
% 0.64/0.89 tff(825,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(826,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(z), z)) | (~b(s(s(s(elem!1))), s(z)))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[825, 824])).
% 0.64/0.89 tff(827,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[826, 206, 357, 796, 735])).
% 0.64/0.89 tff(828,plain,((~b(s(z), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(829,plain,
% 0.64/0.89 (~b(s(s(s(elem!1))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[828, 735, 796])).
% 0.64/0.89 tff(830,plain,
% 0.64/0.89 (r(s(s(s(elem!1))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[372, 829])).
% 0.64/0.89 tff(831,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[551, 830, 820, 543])).
% 0.64/0.89 tff(832,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(z, elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(s(z), z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(833,plain,
% 0.64/0.89 (~b(s(s(s(elem!1))), s(z))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[832, 807, 58, 795, 157])).
% 0.64/0.89 tff(834,plain,
% 0.64/0.89 (r(s(s(s(elem!1))), s(z))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[733, 833])).
% 0.64/0.89 tff(835,plain,
% 0.64/0.89 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[436, 834, 158])).
% 0.64/0.89 tff(836,plain,
% 0.64/0.89 (b(s(s(s(elem!1))), s(elem!1))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[293, 835, 11])).
% 0.64/0.89 tff(837,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(838,plain,
% 0.64/0.89 (((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(839,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[838])).
% 0.64/0.89 tff(840,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 0.64/0.89 inference(transitivity,[status(thm)],[839, 837])).
% 0.64/0.89 tff(841,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), z)))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(842,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), z))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[841, 840])).
% 0.64/0.89 tff(843,plain,
% 0.64/0.89 (~b(s(s(s(elem!1))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[842, 206, 836, 818])).
% 0.64/0.89 tff(844,plain,
% 0.64/0.89 (r(s(s(s(elem!1))), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[372, 843])).
% 0.64/0.89 tff(845,plain,
% 0.64/0.89 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[588, 844, 229])).
% 0.64/0.89 tff(846,plain,
% 0.64/0.89 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[626, 206, 836, 195])).
% 0.64/0.89 tff(847,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[577, 150, 846, 845, 83])).
% 0.64/0.89 tff(848,plain,((~b(s(s(elem!1)), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(z), s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), z)) | (elem!1 = s(z)) | (s(elem!1) = s(z)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(849,plain,
% 0.64/0.89 (~b(s(s(elem!1)), s(elem!1))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[848, 158, 11, 58, 157, 194, 95, 163, 99, 62])).
% 0.64/0.89 tff(850,plain,
% 0.64/0.89 (r(s(s(elem!1)), s(elem!1))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[605, 849, 57])).
% 0.64/0.89 tff(851,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(852,plain,
% 0.64/0.89 (((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(853,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[852])).
% 0.64/0.89 tff(854,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[853, 851])).
% 0.64/0.89 tff(855,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(856,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1)))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[855, 854])).
% 0.64/0.89 tff(857,plain,
% 0.64/0.89 ($false),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[856, 180, 781, 158, 254])).
% 0.64/0.89 tff(858,plain,((~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.64/0.89 tff(859,plain,
% 0.64/0.89 (~r(s(s(elem!1)), s(z))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[858, 850, 158])).
% 0.64/0.89 tff(860,plain,
% 0.64/0.89 (b(s(s(elem!1)), s(z))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[778, 859])).
% 0.64/0.89 tff(861,plain,
% 0.64/0.89 (~r(s(s(elem!1)), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[762, 860, 95, 58, 157, 163, 99, 11, 62])).
% 0.64/0.89 tff(862,plain,
% 0.64/0.89 (b(s(s(elem!1)), z)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[228, 861])).
% 0.64/0.89 tff(863,plain,
% 0.64/0.89 (~r(s(s(s(elem!1))), s(z))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[462, 860, 58, 168, 163, 620, 158, 95, 11, 850])).
% 0.64/0.89 tff(864,plain,
% 0.64/0.89 (b(s(s(s(elem!1))), s(z))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[733, 863])).
% 0.64/0.89 tff(865,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(866,plain,
% 0.64/0.89 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(867,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[866])).
% 0.64/0.89 tff(868,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.89 inference(transitivity,[status(thm)],[867, 865])).
% 0.64/0.89 tff(869,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.64/0.89 inference(quant_inst,[status(thm)],[])).
% 0.64/0.89 tff(870,plain,
% 0.64/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.64/0.89 inference(modus_ponens,[status(thm)],[869, 868])).
% 0.64/0.89 tff(871,plain,
% 0.64/0.89 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[870, 206, 735, 242])).
% 0.64/0.89 tff(872,plain,
% 0.64/0.89 (~(s(elem!1) = elem!1)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[37, 27])).
% 0.64/0.89 tff(873,plain,
% 0.64/0.89 (~(elem!1 = s(elem!1))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[45, 872])).
% 0.64/0.89 tff(874,plain,
% 0.64/0.89 (~(s(s(elem!1)) = s(elem!1))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[56, 873])).
% 0.64/0.89 tff(875,plain,
% 0.64/0.89 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[76, 874])).
% 0.64/0.89 tff(876,plain,
% 0.64/0.89 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[331, 150, 875, 871])).
% 0.64/0.89 tff(877,plain,
% 0.64/0.89 (~b(s(s(s(elem!1))), elem!1)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[741, 206, 157, 735])).
% 0.64/0.89 tff(878,plain,
% 0.64/0.89 (r(s(s(s(elem!1))), elem!1)),
% 0.64/0.89 inference(unit_resolution,[status(thm)],[320, 877, 58])).
% 0.64/0.89 tff(879,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(880,plain,
% 0.64/0.89 (((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 0.64/0.89 inference(rewrite,[status(thm)],[])).
% 0.64/0.89 tff(881,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1))))))),
% 0.64/0.89 inference(monotonicity,[status(thm)],[880])).
% 0.64/0.89 tff(882,plain,
% 0.64/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1)))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[881, 879])).
% 0.74/0.90 tff(883,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(884,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(elem!1, s(s(elem!1))))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[883, 882])).
% 0.74/0.90 tff(885,plain,
% 0.74/0.90 (~b(elem!1, s(s(elem!1)))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[884, 206, 157, 196, 242])).
% 0.74/0.90 tff(886,assumption,(~b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.74/0.90 tff(887,assumption,(~r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.74/0.90 tff(888,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[412, 150, 27, 887, 886])).
% 0.74/0.90 tff(889,plain,(b(elem!1, s(s(elem!1))) | (elem!1 = s(s(elem!1))) | r(elem!1, s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(890,plain,
% 0.74/0.90 (r(elem!1, s(s(elem!1)))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[889, 885, 27])).
% 0.74/0.90 tff(891,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[673, 890, 878, 876])).
% 0.74/0.90 tff(892,plain,((~b(elem!1, s(z))) | (elem!1 = s(s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(893,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[892, 864, 862, 58, 157, 860, 24])).
% 0.74/0.90 tff(894,plain,((~r(s(z), s(elem!1))) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z))) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(z)) | b(s(elem!1), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(895,plain,
% 0.74/0.90 (~r(s(z), s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[894, 90, 157, 95, 11, 58, 62, 156])).
% 0.74/0.90 tff(896,plain,
% 0.74/0.90 (b(s(z), s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[467, 895, 59])).
% 0.74/0.90 tff(897,plain,
% 0.74/0.90 (~b(s(s(elem!1)), s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[214, 196, 95])).
% 0.74/0.90 tff(898,plain,
% 0.74/0.90 (r(s(s(elem!1)), s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[605, 897, 57])).
% 0.74/0.90 tff(899,plain,
% 0.74/0.90 (b(s(s(s(elem!1))), s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[333, 898, 58, 62, 11])).
% 0.74/0.90 tff(900,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(901,plain,
% 0.74/0.90 (((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(902,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1)))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[901])).
% 0.74/0.90 tff(903,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[902, 900])).
% 0.74/0.90 tff(904,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(905,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(z), s(elem!1)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[904, 903])).
% 0.74/0.90 tff(906,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[905, 206, 61, 607, 735])).
% 0.74/0.90 tff(907,plain,((~b(s(z), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(908,plain,
% 0.74/0.90 (~b(s(s(s(elem!1))), s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[907, 899, 607])).
% 0.74/0.90 tff(909,plain,
% 0.74/0.90 (r(s(s(s(elem!1))), s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[733, 908])).
% 0.74/0.90 tff(910,plain,
% 0.74/0.90 (~(z = elem!1)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[239, 90])).
% 0.74/0.90 tff(911,assumption,(b(z, s(z))), introduced(assumption)).
% 0.74/0.90 tff(912,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(913,plain,
% 0.74/0.90 (((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(914,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[913])).
% 0.74/0.90 tff(915,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[914, 912])).
% 0.74/0.90 tff(916,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(elem!1, s(z))) | (~b(z, s(z))) | (~b(elem!1, z)))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(917,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(z, s(z)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[916, 915])).
% 0.74/0.90 tff(918,plain,
% 0.74/0.90 (~b(elem!1, z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[917, 206, 157, 911])).
% 0.74/0.90 tff(919,plain,
% 0.74/0.90 (r(elem!1, z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[387, 918, 288])).
% 0.74/0.90 tff(920,plain,
% 0.74/0.90 (~r(s(elem!1), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[650, 919, 253])).
% 0.74/0.90 tff(921,plain,
% 0.74/0.90 (b(s(elem!1), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[283, 920])).
% 0.74/0.90 tff(922,plain,
% 0.74/0.90 (~b(s(s(elem!1)), s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[214, 921, 196])).
% 0.74/0.90 tff(923,plain,
% 0.74/0.90 (r(s(s(elem!1)), s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[605, 922, 57])).
% 0.74/0.90 tff(924,plain,
% 0.74/0.90 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 0.74/0.90 inference(commutativity,[status(thm)],[])).
% 0.74/0.90 tff(925,plain,
% 0.74/0.90 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 0.74/0.90 inference(symmetry,[status(thm)],[924])).
% 0.74/0.90 tff(926,plain,
% 0.74/0.90 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[925])).
% 0.74/0.90 tff(927,plain,
% 0.74/0.90 (~(z = s(elem!1))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[233, 926])).
% 0.74/0.90 tff(928,plain,
% 0.74/0.90 (~b(z, elem!1)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[563, 206, 157, 911])).
% 0.74/0.90 tff(929,plain,
% 0.74/0.90 (r(z, elem!1)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[556, 928, 109])).
% 0.74/0.90 tff(930,plain,
% 0.74/0.90 (b(s(s(s(elem!1))), s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[333, 923, 58, 62, 11])).
% 0.74/0.90 tff(931,plain,
% 0.74/0.90 (~b(elem!1, s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[396, 930, 288, 18, 253, 58, 921])).
% 0.74/0.90 tff(932,plain,
% 0.74/0.90 (r(elem!1, s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[401, 931, 46])).
% 0.74/0.90 tff(933,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(934,plain,
% 0.74/0.90 (((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(935,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[934])).
% 0.74/0.90 tff(936,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[935, 933])).
% 0.74/0.90 tff(937,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(938,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[937, 936])).
% 0.74/0.90 tff(939,plain,
% 0.74/0.90 ((~r(z, elem!1)) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[938, 180])).
% 0.74/0.90 tff(940,plain,
% 0.74/0.90 (~r(z, s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[939, 932, 929])).
% 0.74/0.90 tff(941,plain,
% 0.74/0.90 ((z = s(elem!1)) | b(z, s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[817, 150, 940])).
% 0.74/0.90 tff(942,plain,
% 0.74/0.90 (b(z, s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[941, 927])).
% 0.74/0.90 tff(943,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 0.74/0.90 tff(944,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(945,plain,
% 0.74/0.90 (((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z)))) <=> ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(946,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(elem!1)))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[945])).
% 0.74/0.90 tff(947,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(elem!1))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[946, 944])).
% 0.74/0.90 tff(948,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(z))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(949,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(z, s(z))) | (~b(s(z), s(elem!1)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[948, 947])).
% 0.74/0.90 tff(950,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[949, 206, 607, 911, 943])).
% 0.74/0.90 tff(951,plain,((~b(s(z), s(elem!1))) | (~b(z, s(z))) | (~b(z, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(952,plain,
% 0.74/0.90 (~b(s(z), s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[951, 942, 911])).
% 0.74/0.90 tff(953,plain,
% 0.74/0.90 (r(s(z), s(elem!1))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[467, 952, 59])).
% 0.74/0.90 tff(954,plain,
% 0.74/0.90 (~b(s(s(elem!1)), s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[462, 953, 243, 65, 288, 253, 58, 921, 11, 923])).
% 0.74/0.90 tff(955,plain,
% 0.74/0.90 (r(s(s(elem!1)), s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[778, 954])).
% 0.74/0.90 tff(956,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[856, 180, 955, 953, 923])).
% 0.74/0.90 tff(957,plain,((~b(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = s(z)) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (s(z) = s(elem!1)) | (~b(z, s(z))) | b(s(elem!1), elem!1) | (~b(s(s(elem!1)), z)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(958,plain,
% 0.74/0.90 (~b(z, s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[957, 909, 11, 62, 65, 58, 157, 59, 196, 910])).
% 0.74/0.90 tff(959,plain,
% 0.74/0.90 (r(z, s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[505, 958])).
% 0.74/0.90 tff(960,plain,
% 0.74/0.90 (~r(s(s(s(elem!1))), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[493, 959, 909])).
% 0.74/0.90 tff(961,plain,
% 0.74/0.90 (b(s(s(s(elem!1))), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[372, 960])).
% 0.74/0.90 tff(962,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[723, 206, 961, 95, 899])).
% 0.74/0.90 tff(963,plain,((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | b(s(elem!1), elem!1) | (elem!1 = s(z)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z))) | (s(z) = s(elem!1)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(964,plain,
% 0.74/0.90 (~b(s(s(elem!1)), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[963, 59, 11, 62, 163, 58, 157, 95, 896])).
% 0.74/0.90 tff(965,plain,
% 0.74/0.90 (r(s(s(elem!1)), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[228, 964])).
% 0.74/0.90 tff(966,plain,
% 0.74/0.90 (~b(s(s(elem!1)), s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[762, 965, 95, 58, 157, 163, 90, 11, 62])).
% 0.74/0.90 tff(967,plain,
% 0.74/0.90 (r(s(s(elem!1)), s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[778, 966])).
% 0.74/0.90 tff(968,plain,
% 0.74/0.90 (~r(s(z), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[789, 967, 965])).
% 0.74/0.90 tff(969,plain,
% 0.74/0.90 (b(s(z), z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[794, 968])).
% 0.74/0.90 tff(970,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(971,plain,
% 0.74/0.90 (((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 0.74/0.90 inference(rewrite,[status(thm)],[])).
% 0.74/0.90 tff(972,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[971])).
% 0.74/0.90 tff(973,plain,
% 0.74/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[972, 970])).
% 0.74/0.90 tff(974,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(975,plain,
% 0.74/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[974, 973])).
% 0.74/0.90 tff(976,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[975, 206, 95, 969, 896])).
% 0.74/0.90 tff(977,plain,((s(z) = s(elem!1)) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(elem!1), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(978,plain,
% 0.74/0.90 (s(z) = elem!1),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[977, 155, 58, 95, 11, 62, 140])).
% 0.74/0.90 tff(979,plain,
% 0.74/0.90 (elem!1 = s(z)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[978, 96])).
% 0.74/0.90 tff(980,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[65, 979])).
% 0.74/0.90 tff(981,plain,((elem!1 = s(z)) | (s(s(s(elem!1))) = elem!1) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | b(s(elem!1), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(982,plain,
% 0.74/0.90 (elem!1 = s(z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[981, 95, 58, 11, 62, 91])).
% 0.74/0.90 tff(983,plain,
% 0.74/0.90 (s(elem!1) = s(s(z))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[982])).
% 0.74/0.90 tff(984,plain,
% 0.74/0.90 (s(s(elem!1)) = s(s(s(z)))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[983])).
% 0.74/0.90 tff(985,plain,
% 0.74/0.90 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[984])).
% 0.74/0.90 tff(986,plain,
% 0.74/0.90 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 0.74/0.90 inference(symmetry,[status(thm)],[985])).
% 0.74/0.90 tff(987,plain,
% 0.74/0.90 (s(s(s(z))) = s(s(elem!1))),
% 0.74/0.90 inference(symmetry,[status(thm)],[984])).
% 0.74/0.90 tff(988,plain,
% 0.74/0.90 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[987, 986])).
% 0.74/0.90 tff(989,plain,
% 0.74/0.90 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 0.74/0.90 inference(symmetry,[status(thm)],[988])).
% 0.74/0.90 tff(990,plain,
% 0.74/0.90 ((~b(s(s(elem!1)), s(s(s(elem!1))))) <=> (~b(s(s(s(z))), s(s(s(s(z))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[989])).
% 0.74/0.90 tff(991,plain,
% 0.74/0.90 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[982])).
% 0.74/0.90 tff(992,plain,
% 0.74/0.90 (~(s(elem!1) = s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[89, 140])).
% 0.74/0.90 tff(993,plain,
% 0.74/0.90 (~(z = elem!1)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[239, 992])).
% 0.74/0.90 tff(994,plain,
% 0.74/0.90 (~(elem!1 = z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[287, 993])).
% 0.74/0.90 tff(995,plain,
% 0.74/0.90 (s(elem!1) = s(s(z))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[159])).
% 0.74/0.90 tff(996,plain,
% 0.74/0.90 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[995])).
% 0.74/0.90 tff(997,plain,
% 0.74/0.90 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[159])).
% 0.74/0.90 tff(998,plain,
% 0.74/0.90 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 0.74/0.90 inference(transitivity,[status(thm)],[997, 996])).
% 0.74/0.90 tff(999,plain,
% 0.74/0.90 (s(z) = elem!1),
% 0.74/0.90 inference(symmetry,[status(thm)],[159])).
% 0.74/0.90 tff(1000,plain,
% 0.74/0.90 (r(s(s(s(s(z)))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[999])).
% 0.74/0.90 tff(1001,plain,
% 0.74/0.90 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(z))),
% 0.74/0.90 inference(symmetry,[status(thm)],[1000])).
% 0.74/0.90 tff(1002,plain,
% 0.74/0.90 (s(s(elem!1)) = s(s(s(z)))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[995])).
% 0.74/0.90 tff(1003,plain,
% 0.74/0.90 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1002])).
% 0.74/0.90 tff(1004,plain,
% 0.74/0.90 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 0.74/0.90 inference(symmetry,[status(thm)],[1003])).
% 0.74/0.90 tff(1005,plain,
% 0.74/0.90 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1004, 159])).
% 0.74/0.90 tff(1006,plain,
% 0.74/0.90 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(s(z)))), elem!1)),
% 0.74/0.90 inference(symmetry,[status(thm)],[1005])).
% 0.74/0.90 tff(1007,plain,
% 0.74/0.90 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), s(z))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[159])).
% 0.74/0.90 tff(1008,plain,
% 0.74/0.90 (r(s(s(s(elem!1))), s(z))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[302, 1007])).
% 0.74/0.90 tff(1009,plain,
% 0.74/0.90 (r(s(s(s(s(z)))), elem!1)),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[1008, 1006])).
% 0.74/0.90 tff(1010,plain,
% 0.74/0.90 (r(s(s(s(s(z)))), s(z))),
% 0.74/0.90 inference(modus_ponens,[status(thm)],[1009, 1001])).
% 0.74/0.90 tff(1011,plain,
% 0.74/0.90 (~(z = elem!1)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[137, 135])).
% 0.74/0.90 tff(1012,plain,
% 0.74/0.90 (s(s(s(z))) = s(s(elem!1))),
% 0.74/0.90 inference(symmetry,[status(thm)],[1002])).
% 0.74/0.90 tff(1013,plain,
% 0.74/0.90 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1012])).
% 0.74/0.90 tff(1014,plain,
% 0.74/0.90 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 0.74/0.90 inference(symmetry,[status(thm)],[1013])).
% 0.74/0.90 tff(1015,plain,
% 0.74/0.90 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 0.74/0.90 inference(monotonicity,[status(thm)],[995])).
% 0.74/0.90 tff(1016,assumption,(b(s(s(s(s(s(s(elem!1)))))), z)), introduced(assumption)).
% 0.74/0.90 tff(1017,plain,
% 0.74/0.90 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(1018,plain,
% 0.74/0.90 (inj_0(s(s(z))) = s(z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1017, 8])).
% 0.74/0.90 tff(1019,plain,
% 0.74/0.90 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1003])).
% 0.74/0.90 tff(1020,plain,
% 0.74/0.90 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(1021,plain,
% 0.74/0.90 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1020, 8])).
% 0.74/0.90 tff(1022,plain,
% 0.74/0.90 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1))))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(1023,plain,
% 0.74/0.90 (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1022, 8])).
% 0.74/0.90 tff(1024,assumption,(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.74/0.90 tff(1025,plain,
% 0.74/0.90 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 0.74/0.90 inference(symmetry,[status(thm)],[1024])).
% 0.74/0.90 tff(1026,plain,
% 0.74/0.90 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[1025, 1003])).
% 0.74/0.90 tff(1027,plain,
% 0.74/0.90 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(z)))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1026])).
% 0.74/0.90 tff(1028,plain,
% 0.74/0.90 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.90 inference(symmetry,[status(thm)],[1027])).
% 0.74/0.90 tff(1029,plain,
% 0.74/0.90 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(1030,plain,
% 0.74/0.90 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1029, 8])).
% 0.74/0.90 tff(1031,plain,
% 0.74/0.90 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.74/0.90 inference(symmetry,[status(thm)],[1030])).
% 0.74/0.90 tff(1032,plain,
% 0.74/0.90 (s(s(s(z))) = s(s(s(s(s(elem!1)))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[1031, 1028, 1023])).
% 0.74/0.90 tff(1033,plain,
% 0.74/0.90 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1032])).
% 0.74/0.90 tff(1034,plain,
% 0.74/0.90 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(1035,plain,
% 0.74/0.90 (inj_0(s(s(s(z)))) = s(s(z))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1034, 8])).
% 0.74/0.90 tff(1036,plain,
% 0.74/0.90 (s(s(z)) = inj_0(s(s(s(z))))),
% 0.74/0.90 inference(symmetry,[status(thm)],[1035])).
% 0.74/0.90 tff(1037,plain,
% 0.74/0.90 (s(s(z)) = s(s(s(s(s(z)))))),
% 0.74/0.90 inference(transitivity,[status(thm)],[1036, 1033, 1021, 1019])).
% 0.74/0.90 tff(1038,plain,
% 0.74/0.90 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(z))))))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1037])).
% 0.74/0.90 tff(1039,plain,
% 0.74/0.90 (inj_0(s(s(s(s(s(z)))))) = inj_0(s(s(z)))),
% 0.74/0.90 inference(symmetry,[status(thm)],[1038])).
% 0.74/0.90 tff(1040,plain,
% 0.74/0.90 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z)))))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(1041,plain,
% 0.74/0.90 (inj_0(s(s(s(s(s(z)))))) = s(s(s(s(z))))),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1040, 8])).
% 0.74/0.90 tff(1042,plain,
% 0.74/0.90 (s(s(s(s(z)))) = inj_0(s(s(s(s(s(z))))))),
% 0.74/0.90 inference(symmetry,[status(thm)],[1041])).
% 0.74/0.90 tff(1043,plain,
% 0.74/0.90 (s(s(s(s(z)))) = s(z)),
% 0.74/0.90 inference(transitivity,[status(thm)],[1042, 1039, 1018])).
% 0.74/0.90 tff(1044,assumption,(s(s(s(s(z)))) = s(z)), introduced(assumption)).
% 0.74/0.90 tff(1045,plain,
% 0.74/0.90 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 0.74/0.90 inference(monotonicity,[status(thm)],[1044])).
% 0.74/0.90 tff(1046,plain,
% 0.74/0.90 (s(s(s(z))) = z),
% 0.74/0.90 inference(transitivity,[status(thm)],[1031, 1045, 106])).
% 0.74/0.90 tff(1047,plain,
% 0.74/0.90 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 0.74/0.90 inference(quant_inst,[status(thm)],[])).
% 0.74/0.90 tff(1048,plain,
% 0.74/0.90 (~(s(s(s(z))) = z)),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1047, 222])).
% 0.74/0.90 tff(1049,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1048, 1046])).
% 0.74/0.90 tff(1050,plain,(~(s(s(s(s(z)))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(1051,plain,
% 0.74/0.90 ($false),
% 0.74/0.90 inference(unit_resolution,[status(thm)],[1050, 1043])).
% 0.74/0.90 tff(1052,plain,((~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.90 tff(1053,plain,
% 0.74/0.90 (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1052, 159])).
% 0.74/0.91 tff(1054,plain,
% 0.74/0.91 (r(elem!1, z) <=> r(s(z), z)),
% 0.74/0.91 inference(monotonicity,[status(thm)],[159])).
% 0.74/0.91 tff(1055,plain,
% 0.74/0.91 (r(s(z), z) <=> r(elem!1, z)),
% 0.74/0.91 inference(symmetry,[status(thm)],[1054])).
% 0.74/0.91 tff(1056,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(z))), introduced(assumption)).
% 0.74/0.91 tff(1057,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1058,plain,
% 0.74/0.91 (((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1059,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1058])).
% 0.74/0.91 tff(1060,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.74/0.91 inference(transitivity,[status(thm)],[1059, 1057])).
% 0.74/0.91 tff(1061,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1062,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1061, 1060])).
% 0.74/0.91 tff(1063,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1062, 206, 1056, 796, 1016])).
% 0.74/0.91 tff(1064,plain,((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(1065,plain,
% 0.74/0.91 (~b(s(z), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1064, 1056, 1016])).
% 0.74/0.91 tff(1066,plain,
% 0.74/0.91 (r(s(z), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[794, 1065])).
% 0.74/0.91 tff(1067,plain,
% 0.74/0.91 (r(elem!1, z)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1066, 1055])).
% 0.74/0.91 tff(1068,plain,
% 0.74/0.91 (~r(s(s(s(elem!1))), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[382, 1067, 302])).
% 0.74/0.91 tff(1069,plain,
% 0.74/0.91 (b(s(s(s(elem!1))), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[372, 1068])).
% 0.74/0.91 tff(1070,plain,
% 0.74/0.91 (s(s(z)) = s(elem!1)),
% 0.74/0.91 inference(symmetry,[status(thm)],[995])).
% 0.74/0.91 tff(1071,plain,
% 0.74/0.91 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1070, 1004])).
% 0.74/0.91 tff(1072,plain,
% 0.74/0.91 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1071])).
% 0.74/0.91 tff(1073,plain,
% 0.74/0.91 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1004])).
% 0.74/0.91 tff(1074,plain,
% 0.74/0.91 (r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(symmetry,[status(thm)],[1073])).
% 0.74/0.91 tff(1075,assumption,(b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.74/0.91 tff(1076,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1077,plain,
% 0.74/0.91 (((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1078,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1077])).
% 0.74/0.91 tff(1079,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.91 inference(transitivity,[status(thm)],[1078, 1076])).
% 0.74/0.91 tff(1080,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1081,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1080, 1079])).
% 0.74/0.91 tff(1082,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1081, 206, 357, 1075, 1016])).
% 0.74/0.91 tff(1083,plain,((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(1084,plain,
% 0.74/0.91 (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1083, 1069, 1016])).
% 0.74/0.91 tff(1085,plain,
% 0.74/0.91 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1086,plain,
% 0.74/0.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1087,plain,
% 0.74/0.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1086, 1085])).
% 0.74/0.91 tff(1088,plain,
% 0.74/0.91 ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1087, 150])).
% 0.74/0.91 tff(1089,plain,
% 0.74/0.91 (r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1088, 1084, 1053])).
% 0.74/0.91 tff(1090,plain,
% 0.74/0.91 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1089, 1074])).
% 0.74/0.91 tff(1091,plain,
% 0.74/0.91 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(z)))),
% 0.74/0.91 inference(commutativity,[status(thm)],[])).
% 0.74/0.91 tff(1092,plain,
% 0.74/0.91 ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(symmetry,[status(thm)],[1091])).
% 0.74/0.91 tff(1093,plain,
% 0.74/0.91 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1092])).
% 0.74/0.91 tff(1094,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(z))), introduced(assumption)).
% 0.74/0.91 tff(1095,plain,
% 0.74/0.91 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(z)))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1094])).
% 0.74/0.91 tff(1096,plain,
% 0.74/0.91 (s(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(symmetry,[status(thm)],[1023])).
% 0.74/0.91 tff(1097,plain,
% 0.74/0.91 (s(s(s(s(s(elem!1))))) = s(z)),
% 0.74/0.91 inference(transitivity,[status(thm)],[1096, 1095, 1018])).
% 0.74/0.91 tff(1098,plain,
% 0.74/0.91 ((s(z) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(z))),
% 0.74/0.91 inference(commutativity,[status(thm)],[])).
% 0.74/0.91 tff(1099,plain,
% 0.74/0.91 ((~(s(z) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(z)))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1098])).
% 0.74/0.91 tff(1100,assumption,(s(z) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.74/0.91 tff(1101,plain,
% 0.74/0.91 (s(s(s(s(s(elem!1))))) = s(z)),
% 0.74/0.91 inference(symmetry,[status(thm)],[1100])).
% 0.74/0.91 tff(1102,plain,
% 0.74/0.91 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(z))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1101])).
% 0.74/0.91 tff(1103,plain,
% 0.74/0.91 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.74/0.91 inference(symmetry,[status(thm)],[1021])).
% 0.74/0.91 tff(1104,plain,
% 0.74/0.91 (s(s(s(s(elem!1)))) = z),
% 0.74/0.91 inference(transitivity,[status(thm)],[1103, 1102, 106])).
% 0.74/0.91 tff(1105,plain,
% 0.74/0.91 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1106,plain,
% 0.74/0.91 (~(s(s(s(s(elem!1)))) = z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1105, 222])).
% 0.74/0.91 tff(1107,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1106, 1104])).
% 0.74/0.91 tff(1108,plain,(~(s(z) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(1109,plain,
% 0.74/0.91 (~(s(s(s(s(s(elem!1))))) = s(z))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1108, 1099])).
% 0.74/0.91 tff(1110,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1109, 1097])).
% 0.74/0.91 tff(1111,plain,(~(s(s(s(s(s(s(elem!1)))))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(1112,plain,
% 0.74/0.91 (~(s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1111, 1093])).
% 0.74/0.91 tff(1113,plain,
% 0.74/0.91 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 0.74/0.91 inference(symmetry,[status(thm)],[1071])).
% 0.74/0.91 tff(1114,plain,
% 0.74/0.91 (~r(s(elem!1), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[650, 170, 374])).
% 0.74/0.91 tff(1115,plain,
% 0.74/0.91 (b(s(elem!1), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[283, 1114])).
% 0.74/0.91 tff(1116,plain,
% 0.74/0.91 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[365, 1115, 357])).
% 0.74/0.91 tff(1117,plain,
% 0.74/0.91 (r(s(elem!1), s(s(s(elem!1))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[354, 1116, 21])).
% 0.74/0.91 tff(1118,plain,
% 0.74/0.91 (r(s(s(z)), s(s(s(s(z)))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1117, 1113])).
% 0.74/0.91 tff(1119,assumption,(r(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.74/0.91 tff(1120,plain,
% 0.74/0.91 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[995])).
% 0.74/0.91 tff(1121,plain,
% 0.74/0.91 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[159])).
% 0.74/0.91 tff(1122,plain,
% 0.74/0.91 (r(s(elem!1), elem!1) <=> r(s(s(z)), s(z))),
% 0.74/0.91 inference(transitivity,[status(thm)],[1121, 1120])).
% 0.74/0.91 tff(1123,plain,
% 0.74/0.91 (r(s(s(z)), s(z))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[170, 1122])).
% 0.74/0.91 tff(1124,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1125,plain,
% 0.74/0.91 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1126,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1125])).
% 0.74/0.91 tff(1127,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.91 inference(transitivity,[status(thm)],[1126, 1124])).
% 0.74/0.91 tff(1128,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1129,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1128, 1127])).
% 0.74/0.91 tff(1130,plain,
% 0.74/0.91 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1129, 180, 1123, 1119])).
% 0.74/0.91 tff(1131,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1130, 1118])).
% 0.74/0.91 tff(1132,plain,((~r(s(elem!1), elem!1)) | (~(elem!1 = s(z))) | (~r(s(s(s(s(z)))), s(z))) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(1133,plain,
% 0.74/0.91 (~r(s(elem!1), elem!1)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1132, 1069, 1010, 18, 159, 1067])).
% 0.74/0.91 tff(1134,plain,
% 0.74/0.91 (b(s(elem!1), elem!1)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[167, 1133, 38])).
% 0.74/0.91 tff(1135,plain,
% 0.74/0.91 (b(s(s(z)), s(z))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1134, 998])).
% 0.74/0.91 tff(1136,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(z))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1137,plain,
% 0.74/0.91 (((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(z))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1138,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(z)))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1137])).
% 0.74/0.91 tff(1139,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(z))))),
% 0.74/0.91 inference(transitivity,[status(thm)],[1138, 1136])).
% 0.74/0.91 tff(1140,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1141,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(z)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1140, 1139])).
% 0.74/0.91 tff(1142,plain,
% 0.74/0.91 (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1141, 206, 1056, 1135])).
% 0.74/0.91 tff(1143,plain,
% 0.74/0.91 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
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% 0.74/0.91 tff(1144,plain,
% 0.74/0.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1145,plain,
% 0.74/0.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(z)), s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1144, 1143])).
% 0.74/0.91 tff(1146,plain,
% 0.74/0.91 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1145, 150, 1142])).
% 0.74/0.91 tff(1147,plain,
% 0.74/0.91 (r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1146, 1112])).
% 0.74/0.91 tff(1148,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1149,plain,
% 0.74/0.91 (((~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1150,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1149])).
% 0.74/0.91 tff(1151,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.91 inference(transitivity,[status(thm)],[1150, 1148])).
% 0.74/0.91 tff(1152,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1153,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1152, 1151])).
% 0.74/0.91 tff(1154,plain,
% 0.74/0.91 ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1153, 180, 1010, 1147])).
% 0.74/0.91 tff(1155,plain,
% 0.74/0.91 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1154, 1090])).
% 0.74/0.91 tff(1156,plain,
% 0.74/0.91 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1155, 1072])).
% 0.74/0.91 tff(1157,plain,
% 0.74/0.91 (b(s(elem!1), s(s(s(elem!1))))),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[354, 1156, 18])).
% 0.74/0.91 tff(1158,plain,
% 0.74/0.91 (~b(s(elem!1), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[365, 1157, 1069])).
% 0.74/0.91 tff(1159,plain,
% 0.74/0.91 (r(s(elem!1), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[283, 1158])).
% 0.74/0.91 tff(1160,plain,
% 0.74/0.91 (r(s(s(z)), z)),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1159, 1015])).
% 0.74/0.91 tff(1161,plain,
% 0.74/0.91 ((s(s(s(z))) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1012, 1070])).
% 0.74/0.91 tff(1162,plain,
% 0.74/0.91 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 0.74/0.91 inference(symmetry,[status(thm)],[1161])).
% 0.74/0.91 tff(1163,plain,
% 0.74/0.91 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(s(z))) = s(s(z))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1162])).
% 0.74/0.91 tff(1164,plain,
% 0.74/0.91 (~(s(s(s(z))) = s(s(z)))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[57, 1163])).
% 0.74/0.91 tff(1165,plain,
% 0.74/0.91 (b(s(s(s(s(z)))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1004, 1070])).
% 0.74/0.91 tff(1166,plain,
% 0.74/0.91 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.91 inference(symmetry,[status(thm)],[1165])).
% 0.74/0.91 tff(1167,plain,
% 0.74/0.91 (b(s(elem!1), elem!1)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[315, 289, 302, 11])).
% 0.74/0.91 tff(1168,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 0.74/0.91 tff(1169,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1170,plain,
% 0.74/0.91 (((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 0.74/0.91 inference(rewrite,[status(thm)],[])).
% 0.74/0.91 tff(1171,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))))),
% 0.74/0.91 inference(monotonicity,[status(thm)],[1170])).
% 0.74/0.91 tff(1172,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)))),
% 0.74/0.91 inference(transitivity,[status(thm)],[1171, 1169])).
% 0.74/0.91 tff(1173,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))))),
% 0.74/0.91 inference(quant_inst,[status(thm)],[])).
% 0.74/0.91 tff(1174,plain,
% 0.74/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))),
% 0.74/0.91 inference(modus_ponens,[status(thm)],[1173, 1172])).
% 0.74/0.91 tff(1175,plain,
% 0.74/0.91 ($false),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1174, 180, 270, 60, 304])).
% 0.74/0.91 tff(1176,plain,((~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.91 tff(1177,plain,
% 0.74/0.91 (~r(s(elem!1), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[1176, 60, 304])).
% 0.74/0.91 tff(1178,plain,
% 0.74/0.91 (b(s(elem!1), z)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[283, 1177])).
% 0.74/0.91 tff(1179,plain,
% 0.74/0.91 (~r(z, elem!1)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[551, 60, 302])).
% 0.74/0.91 tff(1180,plain,
% 0.74/0.91 (b(z, elem!1)),
% 0.74/0.91 inference(unit_resolution,[status(thm)],[556, 1179, 109])).
% 0.74/0.91 tff(1181,plain,
% 0.74/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1182,plain,
% 0.74/0.92 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1183,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1182])).
% 0.74/0.92 tff(1184,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1183, 1181])).
% 0.74/0.92 tff(1185,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1186,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(z, elem!1))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1185, 1184])).
% 0.74/0.92 tff(1187,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1186, 206, 1168, 797, 95])).
% 0.74/0.92 tff(1188,plain,((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1189,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1188, 1180, 1178, 1168])).
% 0.74/0.92 tff(1190,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(elem!1), elem!1)) | (z = elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1191,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1190, 1167, 294, 109, 302, 60])).
% 0.74/0.92 tff(1192,plain,(b(s(s(s(elem!1))), s(elem!1)) | (z = elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1193,plain,
% 0.74/0.92 (~r(s(s(s(elem!1))), z)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1192, 289, 302, 109, 11])).
% 0.74/0.92 tff(1194,plain,
% 0.74/0.92 (b(s(s(s(elem!1))), z)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[372, 1193])).
% 0.74/0.92 tff(1195,plain,
% 0.74/0.92 (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1083, 1194, 1016])).
% 0.74/0.92 tff(1196,plain,
% 0.74/0.92 (r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1088, 1195, 1053])).
% 0.74/0.92 tff(1197,plain,
% 0.74/0.92 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1196, 1074])).
% 0.74/0.92 tff(1198,plain,
% 0.74/0.92 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1004])).
% 0.74/0.92 tff(1199,plain,
% 0.74/0.92 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.92 inference(symmetry,[status(thm)],[1198])).
% 0.74/0.92 tff(1200,plain,
% 0.74/0.92 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[995])).
% 0.74/0.92 tff(1201,plain,
% 0.74/0.92 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1200, 1199])).
% 0.74/0.92 tff(1202,plain,
% 0.74/0.92 (r(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[294, 1201])).
% 0.74/0.92 tff(1203,plain,
% 0.74/0.92 (b(s(s(z)), s(z))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1167, 998])).
% 0.74/0.92 tff(1204,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1205,plain,
% 0.74/0.92 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1206,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1205])).
% 0.74/0.92 tff(1207,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1206, 1204])).
% 0.74/0.92 tff(1208,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1209,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1208, 1207])).
% 0.74/0.92 tff(1210,plain,
% 0.74/0.92 (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1209, 206, 1056, 1203])).
% 0.74/0.92 tff(1211,plain,
% 0.74/0.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1212,plain,
% 0.74/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1213,plain,
% 0.74/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(z))) | b(s(s(s(s(s(s(elem!1)))))), s(s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1212, 1211])).
% 0.74/0.92 tff(1214,plain,
% 0.74/0.92 (r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1213, 150, 1111, 1210])).
% 0.74/0.92 tff(1215,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1216,plain,
% 0.74/0.92 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1217,plain,
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% 0.74/0.92 inference(monotonicity,[status(thm)],[1216])).
% 0.74/0.92 tff(1218,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1217, 1215])).
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% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1220,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 0.74/0.92 tff(1221,plain,
% 0.74/0.92 (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1220, 180, 1214, 1202])).
% 0.74/0.92 tff(1222,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1221, 1197])).
% 0.74/0.92 tff(1223,plain,(b(s(s(s(elem!1))), s(elem!1)) | (~(elem!1 = s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(elem!1))), elem!1)) | (z = elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1224,plain,
% 0.74/0.92 (b(s(s(s(elem!1))), s(elem!1))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1223, 1056, 159, 1016, 302, 109, 11])).
% 0.74/0.92 tff(1225,plain,
% 0.74/0.92 (b(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1224, 1166])).
% 0.74/0.92 tff(1226,plain,
% 0.74/0.92 (b(s(z), s(s(z))) <=> b(s(z), s(elem!1))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1070])).
% 0.74/0.92 tff(1227,plain,
% 0.74/0.92 (b(s(z), s(elem!1)) <=> b(s(z), s(s(z)))),
% 0.74/0.92 inference(symmetry,[status(thm)],[1226])).
% 0.74/0.92 tff(1228,plain,
% 0.74/0.92 (~(s(elem!1) = s(z))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[111, 109])).
% 0.74/0.92 tff(1229,plain,
% 0.74/0.92 (~(s(z) = s(elem!1))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[101, 1228])).
% 0.74/0.92 tff(1230,plain,
% 0.74/0.92 (r(s(z), s(s(z))) <=> r(s(z), s(elem!1))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1070])).
% 0.74/0.92 tff(1231,plain,
% 0.74/0.92 ((~r(s(z), s(s(z)))) <=> (~r(s(z), s(elem!1)))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1230])).
% 0.74/0.92 tff(1232,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1233,plain,
% 0.74/0.92 (((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1234,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1233])).
% 0.74/0.92 tff(1235,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1234, 1232])).
% 0.74/0.92 tff(1236,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(z), s(s(z)))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1237,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), z))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1236, 1235])).
% 0.74/0.92 tff(1238,plain,
% 0.74/0.92 (~r(s(z), s(s(z)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1237, 180, 1066, 1160])).
% 0.74/0.92 tff(1239,plain,
% 0.74/0.92 (~r(s(z), s(elem!1))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1238, 1231])).
% 0.74/0.92 tff(1240,plain,
% 0.74/0.92 (b(s(z), s(elem!1))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[467, 1239, 1229])).
% 0.74/0.92 tff(1241,plain,
% 0.74/0.92 (b(s(z), s(s(z)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1240, 1227])).
% 0.74/0.92 tff(1242,plain,
% 0.74/0.92 (r(s(s(s(s(z)))), s(s(s(z)))) <=> r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1004, 1012])).
% 0.74/0.92 tff(1243,plain,
% 0.74/0.92 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.92 inference(symmetry,[status(thm)],[1242])).
% 0.74/0.92 tff(1244,plain,
% 0.74/0.92 ((~r(s(s(s(elem!1))), s(s(elem!1)))) <=> (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1243])).
% 0.74/0.92 tff(1245,plain,
% 0.74/0.92 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1002])).
% 0.74/0.92 tff(1246,plain,
% 0.74/0.92 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 0.74/0.92 inference(symmetry,[status(thm)],[1245])).
% 0.74/0.92 tff(1247,plain,
% 0.74/0.92 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[999])).
% 0.74/0.92 tff(1248,plain,
% 0.74/0.92 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1247, 1246])).
% 0.74/0.92 tff(1249,plain,
% 0.74/0.92 ((~b(s(z), s(s(s(z))))) <=> (~b(elem!1, s(s(elem!1))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1248])).
% 0.74/0.92 tff(1250,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 0.74/0.92 tff(1251,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.74/0.92 tff(1252,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1253,plain,
% 0.74/0.92 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1254,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1253])).
% 0.74/0.92 tff(1255,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1254, 1252])).
% 0.74/0.92 tff(1256,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1257,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(z))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1256, 1255])).
% 0.74/0.92 tff(1258,plain,
% 0.74/0.92 (~b(s(z), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1257, 206, 1251, 1250])).
% 0.74/0.92 tff(1259,plain,
% 0.74/0.92 (~b(elem!1, s(s(elem!1)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1258, 1249])).
% 0.74/0.92 tff(1260,plain,
% 0.74/0.92 (r(elem!1, s(s(elem!1)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[889, 1259, 27])).
% 0.74/0.92 tff(1261,plain,
% 0.74/0.92 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[673, 1260, 302])).
% 0.74/0.92 tff(1262,plain,
% 0.74/0.92 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1261, 1244])).
% 0.74/0.92 tff(1263,assumption,(b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 0.74/0.92 tff(1264,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1265,plain,
% 0.74/0.92 (((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1266,plain,
% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1265])).
% 0.74/0.92 tff(1267,plain,
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% 0.74/0.92 inference(transitivity,[status(thm)],[1266, 1264])).
% 0.74/0.92 tff(1268,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1269,plain,
% 0.74/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1268, 1267])).
% 0.74/0.92 tff(1270,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[1269, 206, 1251, 1263])).
% 0.74/0.92 tff(1271,assumption,(s(s(s(s(z)))) = s(s(s(z)))), introduced(assumption)).
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% 0.74/0.92 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1003, 1271])).
% 0.74/0.92 tff(1273,plain,
% 0.74/0.92 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 0.74/0.92 inference(commutativity,[status(thm)],[])).
% 0.74/0.92 tff(1274,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 0.74/0.92 tff(1275,plain,
% 0.74/0.92 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(z)) = s(s(s(z))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[995, 1274])).
% 0.74/0.92 tff(1276,plain,
% 0.74/0.92 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(z)))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1275, 1273])).
% 0.74/0.92 tff(1277,plain,
% 0.74/0.92 ((s(s(s(z))) = s(s(z))) <=> (s(elem!1) = s(s(s(elem!1))))),
% 0.74/0.92 inference(symmetry,[status(thm)],[1276])).
% 0.74/0.92 tff(1278,plain,
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% 0.74/0.92 inference(symmetry,[status(thm)],[1274])).
% 0.74/0.92 tff(1279,plain,
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% 0.74/0.92 inference(monotonicity,[status(thm)],[1278])).
% 0.74/0.92 tff(1280,plain,
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% 0.74/0.92 inference(symmetry,[status(thm)],[1279])).
% 0.74/0.92 tff(1281,plain,
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% 0.74/0.92 inference(transitivity,[status(thm)],[1012, 72, 1280, 1035])).
% 0.74/0.92 tff(1282,plain,
% 0.74/0.92 (s(elem!1) = s(s(s(elem!1)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1281, 1277])).
% 0.74/0.92 tff(1283,assumption,(s(s(s(elem!1))) = s(elem!1)), introduced(assumption)).
% 0.74/0.92 tff(1284,plain,
% 0.74/0.92 (s(s(s(elem!1))) = s(s(z))),
% 0.74/0.92 inference(transitivity,[status(thm)],[1283, 995])).
% 0.74/0.92 tff(1285,plain,
% 0.74/0.92 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(z)))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1284])).
% 0.74/0.92 tff(1286,plain,
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% 0.74/0.92 inference(transitivity,[status(thm)],[72, 1285, 1018])).
% 0.74/0.92 tff(1287,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[772, 1286])).
% 0.74/0.92 tff(1288,plain,((~(s(s(s(elem!1))) = s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1289,plain,
% 0.74/0.92 (~(s(s(s(elem!1))) = s(elem!1))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1288, 159])).
% 0.74/0.92 tff(1290,plain,
% 0.74/0.92 (~(s(elem!1) = s(s(s(elem!1))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[17, 1289])).
% 0.74/0.92 tff(1291,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[1290, 1282])).
% 0.74/0.92 tff(1292,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1293,plain,
% 0.74/0.92 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1292, 159])).
% 0.74/0.92 tff(1294,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[1293, 1272])).
% 0.74/0.92 tff(1295,plain,((~(s(s(s(s(z)))) = s(s(s(z))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1296,plain,
% 0.74/0.92 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1295, 159])).
% 0.74/0.92 tff(1297,plain,
% 0.74/0.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1298,plain,
% 0.74/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1299,plain,
% 0.74/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1298, 1297])).
% 0.74/0.92 tff(1300,plain,
% 0.74/0.92 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1299, 150, 1296, 1270])).
% 0.74/0.92 tff(1301,plain,
% 0.74/0.92 ($false),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1300, 1262])).
% 0.74/0.92 tff(1302,plain,((~b(s(s(s(z))), s(s(z)))) | (~(elem!1 = s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1303,plain,
% 0.74/0.92 (~b(s(s(s(z))), s(s(z)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1302, 1241, 302, 24, 159, 1225])).
% 0.74/0.92 tff(1304,plain,
% 0.74/0.92 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 0.74/0.92 inference(rewrite,[status(thm)],[])).
% 0.74/0.92 tff(1305,plain,
% 0.74/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z))))),
% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1306,plain,
% 0.74/0.92 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 0.74/0.92 inference(modus_ponens,[status(thm)],[1305, 1304])).
% 0.74/0.92 tff(1307,plain,
% 0.74/0.92 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1306, 150])).
% 0.74/0.92 tff(1308,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[1307, 1303, 1164])).
% 0.74/0.92 tff(1309,plain,
% 0.74/0.92 (r(s(s(s(z))), z) <=> r(s(s(elem!1)), z)),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1012])).
% 0.74/0.92 tff(1310,plain,
% 0.74/0.92 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 0.74/0.92 inference(symmetry,[status(thm)],[1309])).
% 0.74/0.92 tff(1311,plain,
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% 0.74/0.92 inference(modus_ponens,[status(thm)],[241, 1310])).
% 0.74/0.92 tff(1312,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 0.74/0.92 tff(1313,assumption,(r(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.74/0.92 tff(1314,plain,
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% 0.74/0.92 (((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z)))),
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% 0.74/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), z))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1315])).
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% 0.74/0.92 inference(transitivity,[status(thm)],[1316, 1314])).
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% 0.74/0.92 inference(quant_inst,[status(thm)],[])).
% 0.74/0.92 tff(1319,plain,
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% 0.74/0.92 inference(modus_ponens,[status(thm)],[1318, 1317])).
% 0.74/0.92 tff(1320,plain,
% 0.74/0.92 (~r(s(s(s(z))), z)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1319, 180, 1313, 1312])).
% 0.74/0.92 tff(1321,plain,
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[1320, 1311])).
% 0.74/0.92 tff(1322,plain,((~r(s(s(elem!1)), z)) | (~(elem!1 = s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.92 tff(1323,plain,
% 0.74/0.92 (~r(s(s(elem!1)), z)),
% 0.74/0.92 inference(unit_resolution,[status(thm)],[1322, 1308, 159, 1160])).
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% 0.74/0.92 inference(unit_resolution,[status(thm)],[228, 1323])).
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% 0.74/0.92 inference(modus_ponens,[status(thm)],[1324, 1014])).
% 0.74/0.92 tff(1326,assumption,(s(s(s(z))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.74/0.92 tff(1327,plain,
% 0.74/0.92 (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))),
% 0.74/0.92 inference(symmetry,[status(thm)],[1326])).
% 0.74/0.92 tff(1328,plain,
% 0.74/0.92 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(z))))),
% 0.74/0.92 inference(monotonicity,[status(thm)],[1327])).
% 0.74/0.93 tff(1329,plain,
% 0.74/0.93 (s(s(s(s(s(elem!1))))) = s(s(z))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1096, 1328, 1035])).
% 0.74/0.93 tff(1330,plain,
% 0.74/0.93 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(z)))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1329])).
% 0.74/0.93 tff(1331,plain,
% 0.74/0.93 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.74/0.93 inference(symmetry,[status(thm)],[1330])).
% 0.74/0.93 tff(1332,plain,
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% 0.74/0.93 inference(symmetry,[status(thm)],[1018])).
% 0.74/0.93 tff(1333,plain,
% 0.74/0.93 (s(z) = s(s(s(s(elem!1))))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1332, 1331, 1021])).
% 0.74/0.93 tff(1334,plain,
% 0.74/0.93 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1333])).
% 0.74/0.93 tff(1335,plain,
% 0.74/0.93 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
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% 0.74/0.93 tff(1336,plain,
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% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1337,plain,
% 0.74/0.93 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1336, 8])).
% 0.74/0.93 tff(1338,plain,
% 0.74/0.93 (s(s(s(elem!1))) = inj_0(s(s(s(s(elem!1)))))),
% 0.74/0.93 inference(symmetry,[status(thm)],[1337])).
% 0.74/0.93 tff(1339,plain,
% 0.74/0.93 (s(s(s(elem!1))) = z),
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% 0.74/0.93 tff(1340,plain,
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% 0.74/0.93 tff(1341,plain,(~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(1342,plain,
% 0.74/0.93 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1004])).
% 0.74/0.93 tff(1343,plain,
% 0.74/0.93 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 0.74/0.93 inference(symmetry,[status(thm)],[1342])).
% 0.74/0.93 tff(1344,plain,
% 0.74/0.93 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.93 inference(commutativity,[status(thm)],[])).
% 0.74/0.93 tff(1345,plain,
% 0.74/0.93 ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.74/0.93 inference(symmetry,[status(thm)],[1344])).
% 0.74/0.93 tff(1346,plain,
% 0.74/0.93 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1345])).
% 0.74/0.93 tff(1347,plain,
% 0.74/0.93 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1053, 1346])).
% 0.74/0.93 tff(1348,plain,
% 0.74/0.93 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1004])).
% 0.74/0.93 tff(1349,plain,
% 0.74/0.93 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1348])).
% 0.74/0.93 tff(1350,plain,
% 0.74/0.93 (b(s(s(s(s(z)))), z) <=> b(s(s(s(elem!1))), z)),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1004])).
% 0.74/0.93 tff(1351,plain,
% 0.74/0.93 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 0.74/0.93 inference(symmetry,[status(thm)],[1350])).
% 0.74/0.93 tff(1352,plain,
% 0.74/0.93 (b(s(s(s(s(z)))), z)),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1069, 1351])).
% 0.74/0.93 tff(1353,plain,
% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1354,plain,
% 0.74/0.93 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1355,plain,
% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1354])).
% 0.74/0.93 tff(1356,plain,
% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1355, 1353])).
% 0.74/0.93 tff(1357,plain,
% 0.74/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1357, 1356])).
% 0.74/0.93 tff(1359,plain,
% 0.74/0.93 ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1358, 206, 1016])).
% 0.74/0.93 tff(1360,plain,
% 0.74/0.93 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1359, 1352])).
% 0.74/0.93 tff(1361,plain,
% 0.74/0.93 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1360, 1349])).
% 0.74/0.93 tff(1362,plain,
% 0.74/0.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1363,plain,
% 0.74/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1364,plain,
% 0.74/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1363, 1362])).
% 0.74/0.93 tff(1365,plain,
% 0.74/0.93 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1364, 150])).
% 0.74/0.93 tff(1366,plain,
% 0.74/0.93 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1365, 1361, 1347])).
% 0.74/0.93 tff(1367,plain,
% 0.74/0.93 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1366, 1343])).
% 0.74/0.93 tff(1368,plain,
% 0.74/0.93 (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1209, 206, 1056, 1135])).
% 0.74/0.93 tff(1369,plain,
% 0.74/0.93 (r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1213, 150, 1111, 1368])).
% 0.74/0.93 tff(1370,plain,
% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1371,plain,
% 0.74/0.93 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1372,plain,
% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1371])).
% 0.74/0.93 tff(1373,plain,
% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.93 inference(transitivity,[status(thm)],[1372, 1370])).
% 0.74/0.93 tff(1374,plain,
% 0.74/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1374, 1373])).
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% 0.74/0.93 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1375, 180, 1308, 1369, 1367])).
% 0.74/0.93 tff(1377,plain,
% 0.74/0.93 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1378,plain,
% 0.74/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1379,plain,
% 0.74/0.93 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.93 inference(modus_ponens,[status(thm)],[1378, 1377])).
% 0.74/0.93 tff(1380,plain,
% 0.74/0.93 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1379, 150, 1376, 1341])).
% 0.74/0.93 tff(1381,plain,
% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), z)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1382,plain,
% 0.74/0.93 (((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), z)))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1383,plain,
% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), z))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1382])).
% 0.74/0.93 tff(1384,plain,
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% 0.74/0.93 inference(transitivity,[status(thm)],[1383, 1381])).
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% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.93 inference(modus_ponens,[status(thm)],[1385, 1384])).
% 0.74/0.93 tff(1387,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[1386, 206, 1056, 1016])).
% 0.74/0.93 tff(1388,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[1387, 1380, 1325])).
% 0.74/0.93 tff(1389,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~(elem!1 = s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (z = elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
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% 0.74/0.93 tff(1391,assumption,(s(s(s(s(s(s(elem!1)))))) = s(z)), introduced(assumption)).
% 0.74/0.93 tff(1392,plain,
% 0.74/0.93 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(z))),
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% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
% 0.74/0.93 tff(1395,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[1394, 222])).
% 0.74/0.93 tff(1396,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[1395, 1393])).
% 0.74/0.93 tff(1397,plain,(~(s(s(s(s(s(s(elem!1)))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.93 tff(1398,plain,
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% 0.74/0.93 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.93 inference(modus_ponens,[status(thm)],[1399, 1398])).
% 0.74/0.93 tff(1401,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[1400, 150])).
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% 0.74/0.93 (b(s(s(s(s(s(s(elem!1)))))), s(z)) | r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1401, 1397])).
% 0.74/0.93 tff(1403,plain,
% 0.74/0.93 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1402, 1390])).
% 0.74/0.93 tff(1404,assumption,(r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.74/0.93 tff(1405,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(z))), introduced(assumption)).
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% 0.74/0.93 inference(rewrite,[status(thm)],[])).
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% 0.74/0.93 inference(monotonicity,[status(thm)],[1407])).
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% 0.74/0.93 inference(transitivity,[status(thm)],[1408, 1406])).
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% 0.74/0.93 inference(modus_ponens,[status(thm)],[1410, 1409])).
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% 0.74/0.93 tff(1414,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[1413, 1403, 1008])).
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[1088, 1414, 1053])).
% 0.74/0.93 tff(1416,plain,
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% 0.74/0.93 inference(unit_resolution,[status(thm)],[551, 1417, 302])).
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% 0.74/0.93 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1070, 1004])).
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% 0.74/0.93 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
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% 0.74/0.93 tff(1422,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
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% 0.74/0.93 tff(1424,plain,
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% 0.74/0.93 tff(1425,plain,
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% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(z))))),
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% 0.74/0.93 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(z))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
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% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(z)))))),
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% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(z))))),
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% 0.74/0.93 inference(modus_ponens,[status(thm)],[1431, 1430])).
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% 0.74/0.93 (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.93 inference(unit_resolution,[status(thm)],[1432, 180, 1405, 1422])).
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% 0.74/0.93 tff(1435,plain,
% 0.74/0.93 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
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% 0.74/0.93 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.74/0.93 inference(monotonicity,[status(thm)],[1342])).
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% 0.74/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.93 inference(rewrite,[status(thm)],[])).
% 0.74/0.93 tff(1438,plain,
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% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1489,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1488])).
% 0.74/0.94 tff(1490,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1489, 1487])).
% 0.74/0.94 tff(1491,plain,
% 0.74/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1492,plain,
% 0.74/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1491, 1490])).
% 0.74/0.94 tff(1493,plain,
% 0.74/0.94 ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1492, 206])).
% 0.74/0.94 tff(1494,plain,
% 0.74/0.94 (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1493, 1486, 1482])).
% 0.74/0.94 tff(1495,plain,
% 0.74/0.94 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1145, 150, 1494])).
% 0.74/0.94 tff(1496,plain,
% 0.74/0.94 (r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1495, 1112])).
% 0.74/0.94 tff(1497,plain,
% 0.74/0.94 (b(elem!1, z) <=> b(s(z), z)),
% 0.74/0.94 inference(monotonicity,[status(thm)],[159])).
% 0.74/0.94 tff(1498,plain,
% 0.74/0.94 (~r(elem!1, z)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[382, 1417, 302])).
% 0.74/0.94 tff(1499,plain,
% 0.74/0.94 (b(elem!1, z)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[387, 1498, 135])).
% 0.74/0.94 tff(1500,plain,
% 0.74/0.94 (b(s(z), z)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1499, 1497])).
% 0.74/0.94 tff(1501,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1502,plain,
% 0.74/0.94 (((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1503,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1502])).
% 0.74/0.94 tff(1504,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1503, 1501])).
% 0.74/0.94 tff(1505,plain,
% 0.74/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1506,plain,
% 0.74/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1505, 1504])).
% 0.74/0.94 tff(1507,plain,
% 0.74/0.94 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1506, 206, 1500, 1016])).
% 0.74/0.94 tff(1508,plain,
% 0.74/0.94 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(z))),
% 0.74/0.94 inference(commutativity,[status(thm)],[])).
% 0.74/0.94 tff(1509,plain,
% 0.74/0.94 ((s(s(s(s(s(s(elem!1)))))) = s(z)) <=> (s(z) = s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.94 inference(symmetry,[status(thm)],[1508])).
% 0.74/0.94 tff(1510,plain,
% 0.74/0.94 ((~(s(s(s(s(s(s(elem!1)))))) = s(z))) <=> (~(s(z) = s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1509])).
% 0.74/0.94 tff(1511,plain,
% 0.74/0.94 (~(s(z) = s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1397, 1510])).
% 0.74/0.94 tff(1512,plain,
% 0.74/0.94 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1513,plain,
% 0.74/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1514,plain,
% 0.74/0.94 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1513, 1512])).
% 0.74/0.94 tff(1515,plain,
% 0.74/0.94 ((s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1514, 150])).
% 0.74/0.94 tff(1516,plain,
% 0.74/0.94 (b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1515, 1511])).
% 0.74/0.94 tff(1517,plain,
% 0.74/0.94 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1516, 1507])).
% 0.74/0.94 tff(1518,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1519,plain,
% 0.74/0.94 (((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1520,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1519])).
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% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1520, 1518])).
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% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1522, 1521])).
% 0.74/0.94 tff(1524,plain,
% 0.74/0.94 (~r(s(z), s(s(z)))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1523, 180, 1517, 1496])).
% 0.74/0.94 tff(1525,plain,
% 0.74/0.94 (~r(s(z), s(elem!1))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1524, 1231])).
% 0.74/0.94 tff(1526,plain,
% 0.74/0.94 (b(s(z), s(elem!1))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[467, 1525, 1469])).
% 0.74/0.94 tff(1527,plain,
% 0.74/0.94 (b(s(z), s(s(z)))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1526, 1227])).
% 0.74/0.94 tff(1528,plain,
% 0.74/0.94 (~b(s(s(s(z))), s(s(z)))),
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% 0.74/0.94 tff(1529,plain,
% 0.74/0.94 (r(s(s(s(z))), s(s(z)))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1307, 1528, 1164])).
% 0.74/0.94 tff(1530,plain,
% 0.74/0.94 (~r(s(s(elem!1)), z)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1322, 1529, 159, 1465])).
% 0.74/0.94 tff(1531,plain,
% 0.74/0.94 (b(s(s(elem!1)), z)),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[228, 1530])).
% 0.74/0.94 tff(1532,plain,
% 0.74/0.94 (b(s(s(s(z))), z)),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1531, 1014])).
% 0.74/0.94 tff(1533,plain,
% 0.74/0.94 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1453, 206])).
% 0.74/0.94 tff(1534,plain,
% 0.74/0.94 (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1533, 1482, 1486])).
% 0.74/0.94 tff(1535,plain,
% 0.74/0.94 (r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1213, 150, 1111, 1534])).
% 0.74/0.94 tff(1536,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1537,plain,
% 0.74/0.94 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1538,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(z))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1537])).
% 0.74/0.94 tff(1539,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1538, 1536])).
% 0.74/0.94 tff(1540,plain,
% 0.74/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1541,plain,
% 0.74/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 0.74/0.94 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 0.74/0.94 tff(1542,plain,
% 0.74/0.94 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1541, 180, 1403, 1529, 1535])).
% 0.74/0.94 tff(1543,plain,
% 0.74/0.94 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.94 inference(unit_resolution,[status(thm)],[1379, 150, 1542, 1341])).
% 0.74/0.94 tff(1544,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1545,plain,
% 0.74/0.94 (((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.94 inference(rewrite,[status(thm)],[])).
% 0.74/0.94 tff(1546,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 0.74/0.94 inference(monotonicity,[status(thm)],[1545])).
% 0.74/0.94 tff(1547,plain,
% 0.74/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.94 inference(transitivity,[status(thm)],[1546, 1544])).
% 0.74/0.94 tff(1548,plain,
% 0.74/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.94 inference(quant_inst,[status(thm)],[])).
% 0.74/0.94 tff(1549,plain,
% 0.74/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1548, 1547])).
% 0.74/0.95 tff(1550,plain,
% 0.74/0.95 ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), z))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1549, 206, 1016, 1486])).
% 0.74/0.95 tff(1551,plain,
% 0.74/0.95 ($false),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1550, 1543, 1532])).
% 0.74/0.95 tff(1552,plain,((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~(elem!1 = s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = z) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1553,plain,
% 0.74/0.95 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1552, 159, 302, 135, 11])).
% 0.74/0.95 tff(1554,assumption,(~r(s(s(s(s(s(s(elem!1)))))), z)), introduced(assumption)).
% 0.74/0.95 tff(1555,assumption,(~b(s(s(s(s(s(s(elem!1)))))), z)), introduced(assumption)).
% 0.74/0.95 tff(1556,plain,
% 0.74/0.95 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(elem!1)))))) = z))),
% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
% 0.74/0.95 tff(1557,plain,
% 0.74/0.95 (~(s(s(s(s(s(s(elem!1)))))) = z)),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1556, 222])).
% 0.74/0.95 tff(1558,plain,
% 0.74/0.95 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1559,plain,
% 0.74/0.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
% 0.74/0.95 tff(1560,plain,
% 0.74/0.95 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1559, 1558])).
% 0.74/0.95 tff(1561,plain,
% 0.74/0.95 ($false),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1560, 150, 1557, 1555, 1554])).
% 0.74/0.95 tff(1562,plain,(b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z)), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1563,plain,
% 0.74/0.95 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1562, 1553])).
% 0.74/0.95 tff(1564,assumption,(r(s(s(s(s(s(s(elem!1)))))), z)), introduced(assumption)).
% 0.74/0.95 tff(1565,plain,
% 0.74/0.95 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[1004])).
% 0.74/0.95 tff(1566,plain,
% 0.74/0.95 (b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.95 inference(symmetry,[status(thm)],[1565])).
% 0.74/0.95 tff(1567,plain,
% 0.74/0.95 (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1413, 1405, 1008])).
% 0.74/0.95 tff(1568,plain,
% 0.74/0.95 (b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1088, 1567, 1053])).
% 0.74/0.95 tff(1569,plain,
% 0.74/0.95 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1568, 1566])).
% 0.74/0.95 tff(1570,plain,
% 0.74/0.95 (~r(s(s(z)), s(z))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1456, 1405, 18, 1010, 159])).
% 0.74/0.95 tff(1571,plain,
% 0.74/0.95 (~r(s(elem!1), elem!1)),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1460, 1570, 159])).
% 0.74/0.95 tff(1572,plain,
% 0.74/0.95 (b(s(elem!1), elem!1)),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[167, 1571, 38])).
% 0.74/0.95 tff(1573,plain,
% 0.74/0.95 (b(z, elem!1) <=> b(z, s(z))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[159])).
% 0.74/0.95 tff(1574,plain,
% 0.74/0.95 (b(z, s(z)) <=> b(z, elem!1)),
% 0.74/0.95 inference(symmetry,[status(thm)],[1573])).
% 0.74/0.95 tff(1575,plain,
% 0.74/0.95 (~b(s(elem!1), z)),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1188, 1180, 1168])).
% 0.74/0.95 tff(1576,plain,
% 0.74/0.95 (r(s(elem!1), z)),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[283, 1575])).
% 0.74/0.95 tff(1577,plain,
% 0.74/0.95 (r(s(s(z)), z)),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1576, 1015])).
% 0.74/0.95 tff(1578,plain,
% 0.74/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), z)))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1579,plain,
% 0.74/0.95 (((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), z)))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1580,plain,
% 0.74/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), z))))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[1579])).
% 0.74/0.95 tff(1581,plain,
% 0.74/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), z)))),
% 0.74/0.95 inference(transitivity,[status(thm)],[1580, 1578])).
% 0.74/0.95 tff(1582,plain,
% 0.74/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
% 0.74/0.95 tff(1583,plain,
% 0.74/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(z)), z))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1582, 1581])).
% 0.74/0.95 tff(1584,plain,
% 0.74/0.95 (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1583, 180, 1577, 1564])).
% 0.74/0.95 tff(1585,plain,
% 0.74/0.95 (b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1213, 150, 1111, 1584])).
% 0.74/0.95 tff(1586,assumption,(b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.74/0.95 tff(1587,plain,
% 0.74/0.95 (b(s(s(s(elem!1))), s(elem!1))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1192, 60, 302, 109, 11])).
% 0.74/0.95 tff(1588,plain,
% 0.74/0.95 (b(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1587, 1166])).
% 0.74/0.95 tff(1589,plain,
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% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1590,plain,
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% 0.74/0.95 inference(rewrite,[status(thm)],[])).
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% 0.74/0.95 inference(monotonicity,[status(thm)],[1590])).
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% 0.74/0.95 inference(transitivity,[status(thm)],[1591, 1589])).
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% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
% 0.74/0.95 tff(1594,plain,
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[1593, 1592])).
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1594, 206, 1588, 1586, 1585])).
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% 0.74/0.95 tff(1597,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1596, 1569, 1564, 159, 1572, 109, 302, 11])).
% 0.74/0.95 tff(1598,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[372, 1597])).
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% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1600,plain,
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% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1601,plain,
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[1603, 1602])).
% 0.74/0.95 tff(1605,plain,
% 0.74/0.95 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1604, 180, 1405, 485])).
% 0.74/0.95 tff(1606,assumption,(~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.74/0.95 tff(1607,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1413, 1405, 243])).
% 0.74/0.95 tff(1608,plain,
% 0.74/0.95 (b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1088, 1607, 1606])).
% 0.74/0.95 tff(1609,plain,
% 0.74/0.95 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1083, 1608, 357])).
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1560, 150, 1557, 1609, 1605])).
% 0.74/0.95 tff(1611,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1612,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1611, 1598, 1405, 1053, 1008])).
% 0.74/0.95 tff(1613,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[505, 1612])).
% 0.74/0.95 tff(1614,plain,
% 0.74/0.95 (b(z, elem!1)),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1613, 1574])).
% 0.74/0.95 tff(1615,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1188, 1614, 1572])).
% 0.74/0.95 tff(1616,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[283, 1615])).
% 0.74/0.95 tff(1617,plain,
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[1616, 1015])).
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% 0.74/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), z)))),
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% 0.74/0.95 tff(1619,plain,
% 0.74/0.95 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), z)))),
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% 0.74/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), z))))),
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% 0.74/0.95 inference(transitivity,[status(thm)],[1620, 1618])).
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[1622, 1621])).
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1145, 150, 1624])).
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% 0.74/0.95 tff(1627,assumption,(~b(s(s(z)), s(z))), introduced(assumption)).
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% 0.74/0.95 (b(s(s(s(elem!1))), s(s(z))) <=> b(s(s(s(elem!1))), s(elem!1))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[1070])).
% 0.74/0.95 tff(1629,plain,
% 0.74/0.95 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(s(z)))),
% 0.74/0.95 inference(symmetry,[status(thm)],[1628])).
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% 0.74/0.95 inference(transitivity,[status(thm)],[1630, 84])).
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% 0.74/0.95 inference(monotonicity,[status(thm)],[1633])).
% 0.74/0.95 tff(1635,plain,
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[99, 1634])).
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% 0.74/0.95 inference(monotonicity,[status(thm)],[1070])).
% 0.74/0.95 tff(1638,plain,
% 0.74/0.95 (b(s(s(z)), s(z)) <=> b(s(elem!1), elem!1)),
% 0.74/0.95 inference(transitivity,[status(thm)],[1637, 1636])).
% 0.74/0.95 tff(1639,plain,
% 0.74/0.95 ((~b(s(s(z)), s(z))) <=> (~b(s(elem!1), elem!1))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[1638])).
% 0.74/0.95 tff(1640,plain,
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[1627, 1639])).
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% 0.74/0.95 (r(s(elem!1), elem!1)),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[167, 1640, 1635])).
% 0.74/0.95 tff(1642,plain,
% 0.74/0.95 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[312, 1641, 302])).
% 0.74/0.95 tff(1643,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[293, 1642, 11])).
% 0.74/0.95 tff(1644,plain,
% 0.74/0.95 (b(s(s(s(elem!1))), s(s(z)))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1643, 1629])).
% 0.74/0.95 tff(1645,plain,
% 0.74/0.95 (r(s(s(z)), s(z)) <=> r(s(elem!1), s(z))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[1070])).
% 0.74/0.95 tff(1646,plain,
% 0.74/0.95 (r(s(elem!1), s(z)) <=> r(s(s(z)), s(z))),
% 0.74/0.95 inference(symmetry,[status(thm)],[1645])).
% 0.74/0.95 tff(1647,plain,
% 0.74/0.95 ((~b(s(s(z)), s(z))) <=> (~b(s(elem!1), s(z)))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[1637])).
% 0.74/0.95 tff(1648,plain,
% 0.74/0.95 (~b(s(elem!1), s(z))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1627, 1647])).
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% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1650,plain,
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% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.95 inference(modus_ponens,[status(thm)],[1650, 1649])).
% 0.74/0.95 tff(1652,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1651, 150])).
% 0.74/0.95 tff(1653,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1652, 1648, 99])).
% 0.74/0.95 tff(1654,plain,
% 0.74/0.95 (r(s(s(z)), s(z))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1653, 1646])).
% 0.74/0.95 tff(1655,plain,
% 0.74/0.95 (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1432, 180, 1405, 1654])).
% 0.74/0.95 tff(1656,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1213, 150, 1111, 1655])).
% 0.74/0.95 tff(1657,plain,
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% 0.74/0.95 tff(1658,plain,
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% 0.74/0.95 inference(monotonicity,[status(thm)],[1658])).
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% 0.74/0.95 inference(transitivity,[status(thm)],[1659, 1657])).
% 0.74/0.95 tff(1661,plain,
% 0.74/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
% 0.74/0.95 tff(1662,plain,
% 0.74/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1661, 1660])).
% 0.74/0.95 tff(1663,plain,
% 0.74/0.95 (~b(s(s(s(elem!1))), s(s(z)))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1662, 206, 1075, 1656])).
% 0.74/0.95 tff(1664,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1663, 1644])).
% 0.74/0.95 tff(1665,plain,(b(s(s(z)), s(z)) | (~(elem!1 = s(z))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1666,plain,
% 0.74/0.95 (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1665, 1405, 99, 302, 11, 1627, 159])).
% 0.74/0.95 tff(1667,plain,
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% 0.74/0.95 inference(unit_resolution,[status(thm)],[1088, 1666, 1567, 1053])).
% 0.74/0.95 tff(1668,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (s(elem!1) = s(z)) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | b(s(s(z)), s(z)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.95 tff(1669,plain,
% 0.74/0.95 (b(s(s(z)), s(z))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1668, 1405, 302, 11, 1228, 159])).
% 0.74/0.95 tff(1670,plain,
% 0.74/0.95 ((~b(s(s(s(s(z)))), s(s(z)))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[1165])).
% 0.74/0.95 tff(1671,plain,
% 0.74/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1672,plain,
% 0.74/0.95 (((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.74/0.95 inference(rewrite,[status(thm)],[])).
% 0.74/0.95 tff(1673,plain,
% 0.74/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 0.74/0.95 inference(monotonicity,[status(thm)],[1672])).
% 0.74/0.95 tff(1674,plain,
% 0.74/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.74/0.95 inference(transitivity,[status(thm)],[1673, 1671])).
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% 0.74/0.95 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(z))))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1675, 1674])).
% 0.74/0.95 tff(1677,plain,
% 0.74/0.95 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.95 inference(unit_resolution,[status(thm)],[1676, 206, 1569, 1626])).
% 0.74/0.95 tff(1678,plain,
% 0.74/0.95 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.74/0.95 inference(modus_ponens,[status(thm)],[1677, 1670])).
% 0.74/0.95 tff(1679,plain,
% 0.74/0.95 (r(s(s(s(elem!1))), s(elem!1))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[293, 1678, 11])).
% 0.74/0.96 tff(1680,plain,
% 0.74/0.96 (r(s(s(s(s(z)))), s(s(z)))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1679, 1201])).
% 0.74/0.96 tff(1681,assumption,(b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
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% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1683,plain,
% 0.74/0.96 (((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1684,plain,
% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1683])).
% 0.74/0.96 tff(1685,plain,
% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.96 inference(transitivity,[status(thm)],[1684, 1682])).
% 0.74/0.96 tff(1686,plain,
% 0.74/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(1687,plain,
% 0.74/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1686, 1685])).
% 0.74/0.96 tff(1688,plain,
% 0.74/0.96 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1687, 206, 1681, 1586])).
% 0.74/0.96 tff(1689,assumption,(~(s(s(s(s(z)))) = s(s(s(z))))), introduced(assumption)).
% 0.74/0.96 tff(1690,plain,
% 0.74/0.96 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1299, 150, 1689, 1688])).
% 0.74/0.96 tff(1691,assumption,(r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 0.74/0.96 tff(1692,assumption,(~(s(s(s(z))) = s(s(z)))), introduced(assumption)).
% 0.74/0.96 tff(1693,assumption,(b(s(s(z)), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.74/0.96 tff(1694,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 0.74/0.96 tff(1695,plain,
% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1696,plain,
% 0.74/0.96 (((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1697,plain,
% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1696])).
% 0.74/0.96 tff(1698,plain,
% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.74/0.96 inference(transitivity,[status(thm)],[1697, 1695])).
% 0.74/0.96 tff(1699,plain,
% 0.74/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(1700,plain,
% 0.74/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1699, 1698])).
% 0.74/0.96 tff(1701,plain,
% 0.74/0.96 (~b(s(s(s(z))), s(s(z)))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1700, 206, 1681, 1694, 1693])).
% 0.74/0.96 tff(1702,plain,
% 0.74/0.96 (r(s(s(s(z))), s(s(z)))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1307, 1701, 1692])).
% 0.74/0.96 tff(1703,plain,
% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1704,plain,
% 0.74/0.96 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1705,plain,
% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1704])).
% 0.74/0.96 tff(1706,plain,
% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.96 inference(transitivity,[status(thm)],[1705, 1703])).
% 0.74/0.96 tff(1707,plain,
% 0.74/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(1708,plain,
% 0.74/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1707, 1706])).
% 0.74/0.96 tff(1709,plain,
% 0.74/0.96 ($false),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1708, 180, 1702, 1691, 1690])).
% 0.74/0.96 tff(1710,plain,((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(s(s(z)))) = s(s(s(z)))) | (s(s(s(z))) = s(s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.96 tff(1711,plain,
% 0.74/0.96 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1710, 1680, 1296, 1164, 1669, 1626, 1569])).
% 0.74/0.96 tff(1712,assumption,(~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.74/0.96 tff(1713,assumption,(~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.74/0.96 tff(1714,plain,
% 0.74/0.96 ($false),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1379, 150, 1713, 1712, 1341])).
% 0.74/0.96 tff(1715,plain,(b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.96 tff(1716,plain,
% 0.74/0.96 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1715, 1711])).
% 0.74/0.96 tff(1717,assumption,(s(s(s(z))) = s(z)), introduced(assumption)).
% 0.74/0.96 tff(1718,plain,
% 0.74/0.96 (s(s(elem!1)) = s(z)),
% 0.74/0.96 inference(transitivity,[status(thm)],[1002, 1717])).
% 0.74/0.96 tff(1719,plain,
% 0.74/0.96 ($false),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[772, 1718])).
% 0.74/0.96 tff(1720,plain,((~(s(s(s(z))) = s(z))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.96 tff(1721,plain,
% 0.74/0.96 (~(s(s(s(z))) = s(z))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1720, 159])).
% 0.74/0.96 tff(1722,plain,
% 0.74/0.96 (r(s(s(z)), z) <=> r(s(elem!1), z)),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1070])).
% 0.74/0.96 tff(1723,plain,
% 0.74/0.96 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 0.74/0.96 inference(symmetry,[status(thm)],[1722])).
% 0.74/0.96 tff(1724,plain,
% 0.74/0.96 (r(s(s(z)), z)),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[270, 1723])).
% 0.74/0.96 tff(1725,plain,
% 0.74/0.96 (r(s(s(s(z))), s(s(z))) <=> r(s(s(elem!1)), s(elem!1))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1012, 1070])).
% 0.74/0.96 tff(1726,plain,
% 0.74/0.96 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 0.74/0.96 inference(symmetry,[status(thm)],[1725])).
% 0.74/0.96 tff(1727,plain,
% 0.74/0.96 ((~(s(elem!1) = s(z))) <=> (~(elem!1 = s(elem!1)))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1632])).
% 0.74/0.96 tff(1728,plain,
% 0.74/0.96 (~(elem!1 = s(elem!1))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[99, 1727])).
% 0.74/0.96 tff(1729,plain,
% 0.74/0.96 (~(s(s(elem!1)) = s(elem!1))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[56, 1728])).
% 0.74/0.96 tff(1730,plain,
% 0.74/0.96 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1012, 1070])).
% 0.74/0.96 tff(1731,plain,
% 0.74/0.96 ((~b(s(s(s(z))), s(s(z)))) <=> (~b(s(s(elem!1)), s(elem!1)))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1730])).
% 0.74/0.96 tff(1732,assumption,(b(s(s(s(z))), s(z))), introduced(assumption)).
% 0.74/0.96 tff(1733,plain,
% 0.74/0.96 ((s(s(s(elem!1))) = s(z)) <=> (s(s(s(elem!1))) = elem!1)),
% 0.74/0.96 inference(monotonicity,[status(thm)],[999])).
% 0.74/0.96 tff(1734,plain,
% 0.74/0.96 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(s(s(elem!1))) = elem!1))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1733])).
% 0.74/0.96 tff(1735,plain,
% 0.74/0.96 (~(s(s(s(elem!1))) = elem!1)),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[427, 1734])).
% 0.74/0.96 tff(1736,plain,
% 0.74/0.96 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[159])).
% 0.74/0.96 tff(1737,plain,
% 0.74/0.96 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), elem!1)),
% 0.74/0.96 inference(symmetry,[status(thm)],[1736])).
% 0.74/0.96 tff(1738,plain,
% 0.74/0.96 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(elem!1))), elem!1))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1737])).
% 0.74/0.96 tff(1739,plain,
% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1740,plain,
% 0.74/0.96 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1741,plain,
% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1740])).
% 0.74/0.96 tff(1742,plain,
% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.74/0.96 inference(transitivity,[status(thm)],[1741, 1739])).
% 0.74/0.96 tff(1743,plain,
% 0.74/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(1744,plain,
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% 0.74/0.96 inference(modus_ponens,[status(thm)],[1743, 1742])).
% 0.74/0.96 tff(1745,plain,
% 0.74/0.96 (~b(s(s(s(elem!1))), s(s(s(z))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1744, 206, 735, 1732])).
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% 0.74/0.96 inference(rewrite,[status(thm)],[])).
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% 0.74/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z)))))),
% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
% 0.74/0.96 tff(1748,plain,
% 0.74/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(z)))) | b(s(s(s(elem!1))), s(s(s(z)))) | r(s(s(s(elem!1))), s(s(s(z))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1747, 1746])).
% 0.74/0.96 tff(1749,plain,
% 0.74/0.96 (r(s(s(s(elem!1))), s(s(s(z))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1748, 150, 1293, 1745])).
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% 0.74/0.96 ((s(s(s(z))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 0.74/0.96 inference(commutativity,[status(thm)],[])).
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% 0.74/0.96 ((s(s(s(elem!1))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 0.74/0.96 inference(symmetry,[status(thm)],[1750])).
% 0.74/0.96 tff(1752,plain,
% 0.74/0.96 ((~(s(s(s(elem!1))) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(s(elem!1)))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1751])).
% 0.74/0.96 tff(1753,plain,
% 0.74/0.96 (~(s(s(s(z))) = s(s(s(elem!1))))),
% 0.74/0.96 inference(modus_ponens,[status(thm)],[1293, 1752])).
% 0.74/0.96 tff(1754,plain,
% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
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% 0.74/0.96 (((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(elem!1))))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
% 0.74/0.96 tff(1756,plain,
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% 0.74/0.96 inference(monotonicity,[status(thm)],[1755])).
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% 0.74/0.96 inference(transitivity,[status(thm)],[1756, 1754])).
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% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.96 inference(modus_ponens,[status(thm)],[1758, 1757])).
% 0.74/0.96 tff(1760,plain,
% 0.74/0.96 (~b(s(s(s(z))), s(s(s(elem!1))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1759, 206, 735, 1732])).
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% 0.74/0.96 inference(rewrite,[status(thm)],[])).
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% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.96 inference(modus_ponens,[status(thm)],[1762, 1761])).
% 0.74/0.96 tff(1764,plain,
% 0.74/0.96 ((s(s(s(z))) = s(s(s(elem!1)))) | r(s(s(s(z))), s(s(s(elem!1))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1763, 150, 1760])).
% 0.74/0.96 tff(1765,plain,
% 0.74/0.96 (r(s(s(s(z))), s(s(s(elem!1))))),
% 0.74/0.96 inference(unit_resolution,[status(thm)],[1764, 1753])).
% 0.74/0.96 tff(1766,plain,
% 0.74/0.96 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(elem!1))), s(elem!1))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1070])).
% 0.74/0.96 tff(1767,plain,
% 0.74/0.96 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 0.74/0.96 inference(symmetry,[status(thm)],[1766])).
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% 0.74/0.96 inference(monotonicity,[status(thm)],[1628])).
% 0.74/0.96 tff(1769,plain,
% 0.74/0.96 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 0.74/0.96 inference(symmetry,[status(thm)],[1637])).
% 0.74/0.96 tff(1770,plain,
% 0.74/0.96 (b(s(elem!1), elem!1) <=> b(s(s(z)), s(z))),
% 0.74/0.96 inference(transitivity,[status(thm)],[997, 1769])).
% 0.74/0.96 tff(1771,plain,
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% 0.74/0.96 inference(modus_ponens,[status(thm)],[1772, 1055])).
% 0.74/0.96 tff(1774,plain,
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% 0.74/0.96 inference(unit_resolution,[status(thm)],[650, 1773, 270])).
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% 0.74/0.96 tff(1776,plain,
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% 0.74/0.96 inference(modus_ponens,[status(thm)],[1775, 1770])).
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% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(elem!1))), s(s(z)))))),
% 0.74/0.96 inference(rewrite,[status(thm)],[])).
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% 0.74/0.96 inference(rewrite,[status(thm)],[])).
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% 0.74/0.96 inference(monotonicity,[status(thm)],[1778])).
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% 0.74/0.96 inference(transitivity,[status(thm)],[1779, 1777])).
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% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.96 inference(modus_ponens,[status(thm)],[1781, 1780])).
% 0.74/0.96 tff(1783,plain,
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% 0.74/0.96 tff(1784,plain,
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% 0.74/0.96 tff(1785,plain,
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% 0.74/0.96 tff(1786,plain,
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% 0.74/0.96 inference(modus_ponens,[status(thm)],[1785, 1767])).
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% 0.74/0.96 inference(rewrite,[status(thm)],[])).
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% 0.74/0.96 (((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z))))),
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% 0.74/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 0.74/0.96 inference(monotonicity,[status(thm)],[1788])).
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% 0.74/0.96 inference(transitivity,[status(thm)],[1789, 1787])).
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% 0.74/0.96 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.97 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 0.74/0.97 tff(1793,plain,
% 0.74/0.97 (~b(s(s(s(z))), s(s(z)))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1792, 206, 1776, 1732])).
% 0.74/0.97 tff(1794,plain,
% 0.74/0.97 (~b(s(s(elem!1)), s(elem!1))),
% 0.74/0.97 inference(modus_ponens,[status(thm)],[1793, 1731])).
% 0.74/0.97 tff(1795,plain,
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% 0.74/0.97 tff(1805,plain,
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% 0.74/0.97 tff(1813,plain,
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% 0.74/0.97 tff(1814,plain,
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% 0.74/0.97 inference(transitivity,[status(thm)],[1832, 1830])).
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% 0.74/0.97 inference(rewrite,[status(thm)],[])).
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% 0.74/0.97 (((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~r(s(s(s(elem!1))), s(s(s(z))))) | (~r(s(s(s(elem!1))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1842,plain,
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% 0.74/0.97 inference(monotonicity,[status(thm)],[1841])).
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% 0.74/0.97 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 0.74/0.97 tff(1846,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[1845, 180, 1815, 1839])).
% 0.74/0.97 tff(1847,plain,
% 0.74/0.97 (b(s(s(s(elem!1))), s(s(s(z))))),
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% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1849,plain,
% 0.74/0.97 (((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1850,plain,
% 0.74/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z))))),
% 0.74/0.97 inference(monotonicity,[status(thm)],[1849])).
% 0.74/0.97 tff(1851,plain,
% 0.74/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z)))),
% 0.74/0.97 inference(transitivity,[status(thm)],[1850, 1848])).
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% 0.74/0.97 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(s(s(z))), z))),
% 0.74/0.97 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 0.74/0.97 tff(1854,plain,
% 0.74/0.97 (~b(s(s(s(z))), z)),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1853, 206, 357, 1847])).
% 0.74/0.97 tff(1855,plain,
% 0.74/0.97 ($false),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1854, 1818])).
% 0.74/0.97 tff(1856,plain,((~b(s(s(s(elem!1))), z)) | (~(elem!1 = s(z))) | (~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (s(elem!1) = s(z)) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.97 tff(1857,plain,
% 0.74/0.97 (~b(s(s(s(z))), s(z))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1856, 1616, 1405, 1598, 1228, 1053, 159])).
% 0.74/0.97 tff(1858,assumption,(~(s(s(s(z))) = s(z))), introduced(assumption)).
% 0.74/0.97 tff(1859,assumption,(~b(s(s(s(z))), s(z))), introduced(assumption)).
% 0.74/0.97 tff(1860,assumption,(~r(s(s(s(z))), s(z))), introduced(assumption)).
% 0.74/0.97 tff(1861,plain,
% 0.74/0.97 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)))),
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% 0.74/0.97 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.97 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.74/0.97 inference(modus_ponens,[status(thm)],[1862, 1861])).
% 0.74/0.97 tff(1864,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[1863, 150, 1860, 1859, 1858])).
% 0.74/0.97 tff(1865,plain,(b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z)) | (s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.97 tff(1866,plain,
% 0.74/0.97 (r(s(s(s(z))), s(z))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1865, 1857, 1721])).
% 0.74/0.97 tff(1867,plain,
% 0.74/0.97 (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1583, 180, 1617, 1564])).
% 0.74/0.97 tff(1868,plain,
% 0.74/0.97 (b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1213, 150, 1111, 1867])).
% 0.74/0.97 tff(1869,plain,
% 0.74/0.97 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1442, 180, 1405, 1010])).
% 0.74/0.97 tff(1870,plain,
% 0.74/0.97 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.74/0.97 inference(modus_ponens,[status(thm)],[1869, 1436])).
% 0.74/0.97 tff(1871,plain,
% 0.74/0.97 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1365, 1870, 1347])).
% 0.74/0.97 tff(1872,plain,
% 0.74/0.97 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 0.74/0.97 inference(modus_ponens,[status(thm)],[1871, 1435])).
% 0.74/0.97 tff(1873,plain,
% 0.74/0.97 (~r(s(z), s(elem!1))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[436, 1679, 1008])).
% 0.74/0.97 tff(1874,plain,
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% 0.74/0.97 inference(unit_resolution,[status(thm)],[467, 1873, 1229])).
% 0.74/0.97 tff(1875,plain,
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% 0.74/0.97 inference(modus_ponens,[status(thm)],[1874, 1227])).
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% 0.74/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1877,plain,
% 0.74/0.97 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1878,plain,
% 0.74/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 0.74/0.97 inference(monotonicity,[status(thm)],[1877])).
% 0.74/0.97 tff(1879,plain,
% 0.74/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.97 inference(transitivity,[status(thm)],[1878, 1876])).
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% 0.74/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.97 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.97 inference(modus_ponens,[status(thm)],[1880, 1879])).
% 0.74/0.97 tff(1882,plain,
% 0.74/0.97 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1881, 206, 1875, 1872, 1868])).
% 0.74/0.97 tff(1883,plain,
% 0.74/0.97 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.97 inference(unit_resolution,[status(thm)],[1516, 1882])).
% 0.74/0.97 tff(1884,plain,
% 0.74/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1885,plain,
% 0.74/0.97 (((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.97 inference(rewrite,[status(thm)],[])).
% 0.74/0.97 tff(1886,plain,
% 0.74/0.97 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))))),
% 0.74/0.97 inference(monotonicity,[status(thm)],[1885])).
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% 0.74/0.98 inference(modus_ponens,[status(thm)],[1557, 1955])).
% 0.74/0.98 tff(1957,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1958,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(1959,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1958, 1957])).
% 0.74/0.98 tff(1960,plain,
% 0.74/0.98 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1959, 180, 1899, 1010, 1909])).
% 0.74/0.98 tff(1961,plain,
% 0.74/0.98 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1960, 1436])).
% 0.74/0.98 tff(1962,plain,
% 0.74/0.98 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1365, 1961, 1347])).
% 0.74/0.98 tff(1963,plain,
% 0.74/0.98 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1962, 1435])).
% 0.74/0.98 tff(1964,plain,
% 0.74/0.98 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[1004])).
% 0.74/0.98 tff(1965,plain,
% 0.74/0.98 (b(z, s(s(s(elem!1)))) <=> b(z, s(s(s(s(z)))))),
% 0.74/0.98 inference(symmetry,[status(thm)],[1964])).
% 0.74/0.98 tff(1966,plain,
% 0.74/0.98 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(elem!1))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[1004])).
% 0.74/0.98 tff(1967,plain,
% 0.74/0.98 ((~r(z, s(s(s(s(z)))))) <=> (~r(z, s(s(s(elem!1)))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[1966])).
% 0.74/0.98 tff(1968,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1969,plain,
% 0.74/0.98 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1970,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[1969])).
% 0.74/0.98 tff(1971,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.74/0.98 inference(transitivity,[status(thm)],[1970, 1968])).
% 0.74/0.98 tff(1972,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(1973,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 0.74/0.98 tff(1974,plain,
% 0.74/0.98 ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1973, 180, 1905])).
% 0.74/0.98 tff(1975,plain,
% 0.74/0.98 (~r(z, s(s(s(s(z)))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1974, 1010, 1899])).
% 0.74/0.98 tff(1976,plain,
% 0.74/0.98 (~r(z, s(s(s(elem!1))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1975, 1967])).
% 0.74/0.98 tff(1977,plain,
% 0.74/0.98 ((z = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = z)),
% 0.74/0.98 inference(commutativity,[status(thm)],[])).
% 0.74/0.98 tff(1978,plain,
% 0.74/0.98 ((s(s(s(elem!1))) = z) <=> (z = s(s(s(elem!1))))),
% 0.74/0.98 inference(symmetry,[status(thm)],[1977])).
% 0.74/0.98 tff(1979,plain,
% 0.74/0.98 ((~(s(s(s(elem!1))) = z)) <=> (~(z = s(s(s(elem!1)))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[1978])).
% 0.74/0.98 tff(1980,plain,
% 0.74/0.98 (~(z = s(s(s(elem!1))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[368, 1979])).
% 0.74/0.98 tff(1981,plain,
% 0.74/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1982,plain,
% 0.74/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1)))))),
% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(1983,plain,
% 0.74/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1982, 1981])).
% 0.74/0.98 tff(1984,plain,
% 0.74/0.98 ((z = s(s(s(elem!1)))) | b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1983, 150])).
% 0.74/0.98 tff(1985,plain,
% 0.74/0.98 (b(z, s(s(s(elem!1)))) | r(z, s(s(s(elem!1))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1984, 1980])).
% 0.74/0.98 tff(1986,plain,
% 0.74/0.98 (b(z, s(s(s(elem!1))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1985, 1976])).
% 0.74/0.98 tff(1987,plain,
% 0.74/0.98 (b(z, s(s(s(s(z)))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1986, 1965])).
% 0.74/0.98 tff(1988,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1989,plain,
% 0.74/0.98 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1990,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[1989])).
% 0.74/0.98 tff(1991,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.98 inference(transitivity,[status(thm)],[1990, 1988])).
% 0.74/0.98 tff(1992,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(1993,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1992, 1991])).
% 0.74/0.98 tff(1994,plain,
% 0.74/0.98 ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1993, 206, 1987])).
% 0.74/0.98 tff(1995,plain,
% 0.74/0.98 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1994, 1963])).
% 0.74/0.98 tff(1996,plain,
% 0.74/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(1997,plain,
% 0.74/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(1998,plain,
% 0.74/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[1997, 1996])).
% 0.74/0.98 tff(1999,plain,
% 0.74/0.98 ((z = s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1998, 150, 1995])).
% 0.74/0.98 tff(2000,plain,
% 0.74/0.98 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1999, 1956])).
% 0.74/0.98 tff(2001,plain,
% 0.74/0.98 (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1141, 206, 1907, 1203])).
% 0.74/0.98 tff(2002,plain,
% 0.74/0.98 ((s(s(z)) = s(s(s(s(s(s(elem!1))))))) | r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[1145, 150, 2001])).
% 0.74/0.98 tff(2003,plain,
% 0.74/0.98 (r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[2002, 1112])).
% 0.74/0.98 tff(2004,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(z)))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(2005,plain,
% 0.74/0.98 (((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(z))))) <=> ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(z)))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(2006,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(z))))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[2005])).
% 0.74/0.98 tff(2007,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(z)))))),
% 0.74/0.98 inference(transitivity,[status(thm)],[2006, 2004])).
% 0.74/0.98 tff(2008,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(z)))))),
% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(2009,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(z))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[2008, 2007])).
% 0.74/0.98 tff(2010,plain,
% 0.74/0.98 (~r(z, s(s(z)))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[2009, 180, 2003, 2000])).
% 0.74/0.98 tff(2011,plain,
% 0.74/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(2012,plain,
% 0.74/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z))))),
% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(2013,plain,
% 0.74/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[2012, 2011])).
% 0.74/0.98 tff(2014,plain,
% 0.74/0.98 ((z = s(s(z))) | b(z, s(s(z)))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[2013, 150, 2010])).
% 0.74/0.98 tff(2015,plain,
% 0.74/0.98 (b(z, s(s(z)))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[2014, 1952])).
% 0.74/0.98 tff(2016,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(2017,plain,
% 0.74/0.98 (((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(2018,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[2017])).
% 0.74/0.98 tff(2019,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 0.74/0.98 inference(transitivity,[status(thm)],[2018, 2016])).
% 0.74/0.98 tff(2020,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), z)))),
% 0.74/0.98 inference(quant_inst,[status(thm)],[])).
% 0.74/0.98 tff(2021,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 0.74/0.98 inference(modus_ponens,[status(thm)],[2020, 2019])).
% 0.74/0.98 tff(2022,plain,
% 0.74/0.98 ((~b(s(z), z)) | (~b(s(z), s(s(z))))),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[2021, 206, 2015])).
% 0.74/0.98 tff(2023,plain,
% 0.74/0.98 (~b(s(z), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[2022, 1946])).
% 0.74/0.98 tff(2024,plain,
% 0.74/0.98 (r(s(z), z)),
% 0.74/0.98 inference(unit_resolution,[status(thm)],[794, 2023])).
% 0.74/0.98 tff(2025,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(2026,plain,
% 0.74/0.98 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.98 inference(rewrite,[status(thm)],[])).
% 0.74/0.98 tff(2027,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))))),
% 0.74/0.98 inference(monotonicity,[status(thm)],[2026])).
% 0.74/0.98 tff(2028,plain,
% 0.74/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.98 inference(transitivity,[status(thm)],[2027, 2025])).
% 0.74/0.98 tff(2029,plain,
% 0.74/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2030,plain,
% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2029, 2028])).
% 0.74/0.99 tff(2031,plain,
% 0.74/0.99 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2030, 180, 2024, 1915])).
% 0.74/0.99 tff(2032,plain,
% 0.74/0.99 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1516, 2031])).
% 0.74/0.99 tff(2033,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2034,plain,
% 0.74/0.99 (((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2035,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2034])).
% 0.74/0.99 tff(2036,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2035, 2033])).
% 0.74/0.99 tff(2037,plain,
% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(z))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2038,plain,
% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(s(z))), s(s(z))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 0.74/0.99 tff(2039,plain,
% 0.74/0.99 (~b(s(s(s(z))), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2038, 206, 2032, 1939, 1946])).
% 0.74/0.99 tff(2040,plain,
% 0.74/0.99 (r(s(s(s(z))), s(z))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1865, 2039, 1721])).
% 0.74/0.99 tff(2041,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 0.74/0.99 tff(2042,assumption,(r(s(s(s(z))), s(z))), introduced(assumption)).
% 0.74/0.99 tff(2043,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2044,plain,
% 0.74/0.99 (((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2045,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2044])).
% 0.74/0.99 tff(2046,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2045, 2043])).
% 0.74/0.99 tff(2047,plain,
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% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2048,plain,
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% 0.74/0.99 inference(modus_ponens,[status(thm)],[2047, 2046])).
% 0.74/0.99 tff(2049,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2048, 180, 485, 2042, 2041])).
% 0.74/0.99 tff(2050,plain,((~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(2051,plain,
% 0.74/0.99 (~r(s(s(s(z))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2050, 2040, 1905])).
% 0.74/0.99 tff(2052,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2051, 1943])).
% 0.74/0.99 tff(2053,plain,(b(s(s(s(elem!1))), s(elem!1)) | (~(elem!1 = s(z))) | (~b(s(elem!1), z)) | (z = elem!1) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(2054,plain,
% 0.74/0.99 (~b(s(elem!1), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2053, 289, 159, 109, 302, 11])).
% 0.74/0.99 tff(2055,plain,
% 0.74/0.99 (r(s(elem!1), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[283, 2054])).
% 0.74/0.99 tff(2056,plain,
% 0.74/0.99 (r(s(s(z)), z)),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2055, 1015])).
% 0.74/0.99 tff(2057,plain,
% 0.74/0.99 (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1583, 180, 2056, 1564])).
% 0.74/0.99 tff(2058,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[1213, 150, 1111, 2057, 1894])).
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% 0.74/0.99 tff(2060,plain,
% 0.74/0.99 (b(s(s(s(elem!1))), s(elem!1))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2059, 1563, 159, 1011, 302, 11])).
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[1891, 159, 11, 1563, 1011, 302])).
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[1402, 2061])).
% 0.74/0.99 tff(2063,plain,
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% 0.74/0.99 inference(modus_ponens,[status(thm)],[61, 1166])).
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% 0.74/0.99 inference(modus_ponens,[status(thm)],[520, 1163])).
% 0.74/0.99 tff(2065,plain,
% 0.74/0.99 (r(s(z), s(elem!1)) <=> r(s(z), s(s(z)))),
% 0.74/0.99 inference(symmetry,[status(thm)],[1230])).
% 0.74/0.99 tff(2066,plain,
% 0.74/0.99 (r(elem!1, s(elem!1)) <=> r(s(z), s(elem!1))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[159])).
% 0.74/0.99 tff(2067,plain,
% 0.74/0.99 (r(elem!1, s(elem!1)) <=> r(s(z), s(s(z)))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2066, 2065])).
% 0.74/0.99 tff(2068,plain,
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% 0.74/0.99 tff(2069,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[1129, 180, 2068, 1119])).
% 0.74/0.99 tff(2070,plain,
% 0.74/0.99 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2069, 1072])).
% 0.74/0.99 tff(2071,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[354, 2070, 21])).
% 0.74/0.99 tff(2072,plain,
% 0.74/0.99 (b(s(s(z)), s(s(s(s(z)))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2071, 1421])).
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% 0.74/0.99 inference(monotonicity,[status(thm)],[1226])).
% 0.74/0.99 tff(2074,assumption,(b(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
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% 0.74/0.99 inference(modus_ponens,[status(thm)],[270, 1015])).
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% 0.74/0.99 (~r(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1826, 180, 2075, 1564])).
% 0.74/0.99 tff(2077,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[1145, 150, 2076])).
% 0.74/0.99 tff(2078,plain,
% 0.74/0.99 (b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2077, 1112])).
% 0.74/0.99 tff(2079,plain,
% 0.74/0.99 (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1583, 180, 2075, 1564])).
% 0.74/0.99 tff(2080,plain,
% 0.74/0.99 (b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1213, 150, 1111, 2079])).
% 0.74/0.99 tff(2081,plain,
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% 0.74/0.99 inference(rewrite,[status(thm)],[])).
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% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2083,plain,
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% 0.74/0.99 inference(transitivity,[status(thm)],[2083, 2081])).
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% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.99 inference(modus_ponens,[status(thm)],[2085, 2084])).
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[2086, 206, 1263, 2080])).
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% 0.74/0.99 inference(modus_ponens,[status(thm)],[2087, 1349])).
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% 0.74/0.99 inference(modus_ponens,[status(thm)],[2089, 1343])).
% 0.74/0.99 tff(2091,plain,
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% 0.74/0.99 inference(monotonicity,[status(thm)],[1004])).
% 0.74/0.99 tff(2092,plain,
% 0.74/0.99 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), s(s(s(s(z)))))),
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% 0.74/0.99 tff(2093,plain,
% 0.74/0.99 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[159])).
% 0.74/0.99 tff(2094,plain,
% 0.74/0.99 (b(s(z), s(s(s(s(z))))) <=> b(elem!1, s(s(s(elem!1))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[999, 1004])).
% 0.74/0.99 tff(2095,plain,
% 0.74/0.99 ((~b(s(z), s(s(s(s(z)))))) <=> (~b(elem!1, s(s(s(elem!1)))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2094])).
% 0.74/0.99 tff(2096,plain,
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% 0.74/0.99 inference(monotonicity,[status(thm)],[1565])).
% 0.74/0.99 tff(2097,plain,
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[1594, 206, 1263, 2080])).
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% 0.74/0.99 (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2097, 2096])).
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% 0.74/0.99 inference(unit_resolution,[status(thm)],[1088, 2098, 1053])).
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% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
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% 0.74/0.99 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
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% 0.74/0.99 inference(monotonicity,[status(thm)],[2101])).
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% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
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% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2104, 2103])).
% 0.74/0.99 tff(2106,plain,
% 0.74/0.99 ($false),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2105, 180, 60, 1404, 1564])).
% 0.74/0.99 tff(2107,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/0.99 tff(2108,plain,
% 0.74/0.99 (~r(s(s(s(elem!1))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2107, 2099, 1564])).
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% 0.74/0.99 (b(s(s(s(elem!1))), z)),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[372, 2108])).
% 0.74/0.99 tff(2110,plain,
% 0.74/0.99 (b(s(s(s(s(z)))), z)),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2109, 1351])).
% 0.74/0.99 tff(2111,plain,
% 0.74/0.99 (b(s(z), z)),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[652, 1497])).
% 0.74/0.99 tff(2112,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2113,plain,
% 0.74/0.99 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2114,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2113])).
% 0.74/0.99 tff(2115,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2114, 2112])).
% 0.74/0.99 tff(2116,plain,
% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2117,plain,
% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2116, 2115])).
% 0.74/0.99 tff(2118,plain,
% 0.74/0.99 ((~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2117, 206, 2111])).
% 0.74/0.99 tff(2119,plain,
% 0.74/0.99 (~b(s(z), s(s(s(s(z)))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2118, 2110])).
% 0.74/0.99 tff(2120,plain,
% 0.74/0.99 (~b(elem!1, s(s(s(elem!1))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2119, 2095])).
% 0.74/0.99 tff(2121,plain,
% 0.74/0.99 (r(elem!1, s(s(s(elem!1))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[533, 2120, 508])).
% 0.74/0.99 tff(2122,plain,
% 0.74/0.99 (r(s(z), s(s(s(elem!1))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2121, 2093])).
% 0.74/0.99 tff(2123,plain,
% 0.74/0.99 (r(s(z), s(s(s(s(z)))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2122, 2092])).
% 0.74/0.99 tff(2124,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2125,plain,
% 0.74/0.99 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2126,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2125])).
% 0.74/0.99 tff(2127,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2126, 2124])).
% 0.74/0.99 tff(2128,plain,
% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/0.99 inference(quant_inst,[status(thm)],[])).
% 0.74/0.99 tff(2129,plain,
% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.99 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 0.74/0.99 tff(2130,plain,
% 0.74/0.99 ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2129, 180])).
% 0.74/0.99 tff(2131,plain,
% 0.74/0.99 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[2130, 2123, 2090])).
% 0.74/0.99 tff(2132,plain,
% 0.74/0.99 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.74/0.99 inference(unit_resolution,[status(thm)],[1516, 2131])).
% 0.74/0.99 tff(2133,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2134,plain,
% 0.74/0.99 (((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.99 inference(rewrite,[status(thm)],[])).
% 0.74/0.99 tff(2135,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.74/0.99 inference(monotonicity,[status(thm)],[2134])).
% 0.74/0.99 tff(2136,plain,
% 0.74/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/0.99 inference(transitivity,[status(thm)],[2135, 2133])).
% 0.74/0.99 tff(2137,plain,
% 0.74/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2138,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 0.74/1.00 tff(2139,plain,
% 0.74/1.00 (~b(s(z), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2138, 206, 2132, 2078, 2074])).
% 0.74/1.00 tff(2140,plain,
% 0.74/1.00 (~b(s(z), s(elem!1))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2139, 2073])).
% 0.74/1.00 tff(2141,plain,
% 0.74/1.00 (r(s(z), s(elem!1))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[467, 2140, 1469])).
% 0.74/1.00 tff(2142,plain,
% 0.74/1.00 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2099, 1074])).
% 0.74/1.00 tff(2143,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2144,plain,
% 0.74/1.00 (((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))) <=> ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2145,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2144])).
% 0.74/1.00 tff(2146,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[2145, 2143])).
% 0.74/1.00 tff(2147,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z)))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2148,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2147, 2146])).
% 0.74/1.00 tff(2149,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2148, 180, 485, 1422, 1312])).
% 0.74/1.00 tff(2150,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(2151,plain,
% 0.74/1.00 (~r(z, s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2150, 2075, 2068])).
% 0.74/1.00 tff(2152,plain,
% 0.74/1.00 (b(z, s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[505, 2151])).
% 0.74/1.00 tff(2153,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2154,plain,
% 0.74/1.00 (((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(z, s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2155,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2154])).
% 0.74/1.00 tff(2156,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[2155, 2153])).
% 0.74/1.00 tff(2157,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2158,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2157, 2156])).
% 0.74/1.00 tff(2159,plain,
% 0.74/1.00 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2158, 206, 1056, 2152])).
% 0.74/1.00 tff(2160,plain,
% 0.74/1.00 ((z = s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1998, 150, 2159])).
% 0.74/1.00 tff(2161,plain,
% 0.74/1.00 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2160, 1956])).
% 0.74/1.00 tff(2162,plain,
% 0.74/1.00 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[1012])).
% 0.74/1.00 tff(2163,plain,
% 0.74/1.00 (b(z, s(s(elem!1))) <=> b(z, s(s(s(z))))),
% 0.74/1.00 inference(symmetry,[status(thm)],[2162])).
% 0.74/1.00 tff(2164,plain,
% 0.74/1.00 (r(z, s(s(elem!1))) <=> r(z, s(s(s(z))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[1002])).
% 0.74/1.00 tff(2165,plain,
% 0.74/1.00 (r(z, s(s(s(z)))) <=> r(z, s(s(elem!1)))),
% 0.74/1.00 inference(symmetry,[status(thm)],[2164])).
% 0.74/1.00 tff(2166,plain,
% 0.74/1.00 ((~r(z, s(s(s(z))))) <=> (~r(z, s(s(elem!1))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2165])).
% 0.74/1.00 tff(2167,assumption,(r(z, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.74/1.00 tff(2168,assumption,(r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.74/1.00 tff(2169,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2170,plain,
% 0.74/1.00 (((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2171,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1))))))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2170])).
% 0.74/1.00 tff(2172,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[2171, 2169])).
% 0.74/1.00 tff(2173,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(z))))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2174,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(s(s(s(s(s(elem!1))))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2173, 2172])).
% 0.74/1.00 tff(2175,plain,
% 0.74/1.00 (~r(z, s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2174, 180, 2168, 2167])).
% 0.74/1.00 tff(2176,plain,
% 0.74/1.00 (~r(z, s(s(elem!1)))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2175, 2166])).
% 0.74/1.00 tff(2177,plain,
% 0.74/1.00 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 0.74/1.00 inference(commutativity,[status(thm)],[])).
% 0.74/1.00 tff(2178,plain,
% 0.74/1.00 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 0.74/1.00 inference(symmetry,[status(thm)],[2177])).
% 0.74/1.00 tff(2179,plain,
% 0.74/1.00 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2178])).
% 0.74/1.00 tff(2180,plain,
% 0.74/1.00 (~(z = s(s(elem!1)))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[224, 2179])).
% 0.74/1.00 tff(2181,plain,
% 0.74/1.00 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2182,plain,
% 0.74/1.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2183,plain,
% 0.74/1.00 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2182, 2181])).
% 0.74/1.00 tff(2184,plain,
% 0.74/1.00 ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2183, 150])).
% 0.74/1.00 tff(2185,plain,
% 0.74/1.00 (b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2184, 2180])).
% 0.74/1.00 tff(2186,plain,
% 0.74/1.00 (b(z, s(s(elem!1)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2185, 2176])).
% 0.74/1.00 tff(2187,plain,
% 0.74/1.00 (b(z, s(s(s(z))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2186, 2163])).
% 0.74/1.00 tff(2188,assumption,(r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.74/1.00 tff(2189,assumption,(r(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 0.74/1.00 tff(2190,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2191,plain,
% 0.74/1.00 (((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2192,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2191])).
% 0.74/1.00 tff(2193,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[2192, 2190])).
% 0.74/1.00 tff(2194,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2195,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2194, 2193])).
% 0.74/1.00 tff(2196,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2195, 180, 2168, 2188, 2189])).
% 0.74/1.00 tff(2197,plain,((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(2198,plain,
% 0.74/1.00 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2197, 2168, 2188])).
% 0.74/1.00 tff(2199,plain,
% 0.74/1.00 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1299, 150, 1296, 2198])).
% 0.74/1.00 tff(2200,assumption,(b(s(s(s(s(z)))), z)), introduced(assumption)).
% 0.74/1.00 tff(2201,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2202,plain,
% 0.74/1.00 (((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2203,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2202])).
% 0.74/1.00 tff(2204,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[2203, 2201])).
% 0.74/1.00 tff(2205,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), z)))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2206,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2205, 2204])).
% 0.74/1.00 tff(2207,plain,
% 0.74/1.00 ($false),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2206, 206, 2200, 2199, 2187])).
% 0.74/1.00 tff(2208,plain,((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = s(z))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.00 tff(2209,plain,
% 0.74/1.00 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2208, 2110, 159, 2161, 2142])).
% 0.74/1.00 tff(2210,plain,
% 0.74/1.00 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1715, 2209])).
% 0.74/1.00 tff(2211,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2212,plain,
% 0.74/1.00 (((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2213,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2212])).
% 0.74/1.00 tff(2214,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[2213, 2211])).
% 0.74/1.00 tff(2215,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(z))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2216,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 0.74/1.00 tff(2217,plain,
% 0.74/1.00 (~b(s(s(s(z))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2216, 206, 2132, 2210])).
% 0.74/1.00 tff(2218,plain,
% 0.74/1.00 (r(s(s(s(z))), s(z))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1865, 2217, 1721])).
% 0.74/1.00 tff(2219,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2220,plain,
% 0.74/1.00 (((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2221,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2220])).
% 0.74/1.00 tff(2222,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[2221, 2219])).
% 0.74/1.00 tff(2223,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(z)))))),
% 0.74/1.00 inference(quant_inst,[status(thm)],[])).
% 0.74/1.00 tff(2224,plain,
% 0.74/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z))))))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[2223, 2222])).
% 0.74/1.00 tff(2225,plain,
% 0.74/1.00 (~b(s(s(s(z))), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[2224, 206, 2210, 2078, 2074])).
% 0.74/1.00 tff(2226,plain,
% 0.74/1.00 (r(s(s(s(z))), s(s(z)))),
% 0.74/1.00 inference(unit_resolution,[status(thm)],[1307, 2225, 1692])).
% 0.74/1.00 tff(2227,plain,
% 0.74/1.00 (r(s(z), s(s(z)))),
% 0.74/1.00 inference(modus_ponens,[status(thm)],[158, 2065])).
% 0.74/1.00 tff(2228,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2229,plain,
% 0.74/1.00 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.74/1.00 inference(rewrite,[status(thm)],[])).
% 0.74/1.00 tff(2230,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 0.74/1.00 inference(monotonicity,[status(thm)],[2229])).
% 0.74/1.00 tff(2231,plain,
% 0.74/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.74/1.00 inference(transitivity,[status(thm)],[2230, 2228])).
% 0.74/1.01 tff(2232,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(z))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(2233,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2232, 2231])).
% 0.74/1.01 tff(2234,plain,
% 0.74/1.01 (~r(s(z), s(s(z)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2233, 180, 2042, 1313])).
% 0.74/1.01 tff(2235,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2234, 2227])).
% 0.74/1.01 tff(2236,plain,((~r(s(z), s(elem!1))) | (~(elem!1 = s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(2237,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2236, 2226, 2218, 2141, 159])).
% 0.74/1.01 tff(2238,plain,((~r(s(elem!1), z)) | (~(elem!1 = s(z))) | (s(s(s(z))) = s(s(z))) | (~b(s(s(z)), s(s(s(s(z)))))) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (elem!1 = z) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(2239,plain,
% 0.74/1.01 (~r(s(elem!1), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2238, 2072, 2064, 159, 419, 1564, 2063, 1056, 135, 170])).
% 0.74/1.01 tff(2240,plain,
% 0.74/1.01 (b(s(elem!1), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[283, 2239])).
% 0.74/1.01 tff(2241,plain,
% 0.74/1.01 (~b(elem!1, s(elem!1))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[396, 2240, 135, 21, 170, 58, 61])).
% 0.74/1.01 tff(2242,plain,
% 0.74/1.01 (r(elem!1, s(elem!1))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[401, 2241, 519])).
% 0.74/1.01 tff(2243,plain,
% 0.74/1.01 (r(s(z), s(s(z)))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2242, 2067])).
% 0.74/1.01 tff(2244,plain,
% 0.74/1.01 (~b(s(s(s(elem!1))), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[365, 2240, 2071])).
% 0.74/1.01 tff(2245,plain,
% 0.74/1.01 (r(s(s(s(elem!1))), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[372, 2244])).
% 0.74/1.01 tff(2246,plain,
% 0.74/1.01 (r(s(s(s(s(z)))), z)),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2245, 1471])).
% 0.74/1.01 tff(2247,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2248,plain,
% 0.74/1.01 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2249,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[2248])).
% 0.74/1.01 tff(2250,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.74/1.01 inference(transitivity,[status(thm)],[2249, 2247])).
% 0.74/1.01 tff(2251,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(2252,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2251, 2250])).
% 0.74/1.01 tff(2253,plain,
% 0.74/1.01 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2252, 180, 1564])).
% 0.74/1.01 tff(2254,plain,
% 0.74/1.01 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2253, 2246])).
% 0.74/1.01 tff(2255,plain,
% 0.74/1.01 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2254, 1436])).
% 0.74/1.01 tff(2256,plain,
% 0.74/1.01 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1365, 2255, 1347])).
% 0.74/1.01 tff(2257,plain,
% 0.74/1.01 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2256, 1435])).
% 0.74/1.01 tff(2258,plain,
% 0.74/1.01 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 0.74/1.01 inference(monotonicity,[status(thm)],[1070])).
% 0.74/1.01 tff(2259,plain,
% 0.74/1.01 (b(s(elem!1), z) <=> b(s(s(z)), z)),
% 0.74/1.01 inference(symmetry,[status(thm)],[2258])).
% 0.74/1.01 tff(2260,plain,
% 0.74/1.01 (b(s(s(z)), z)),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2240, 2259])).
% 0.74/1.01 tff(2261,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2262,plain,
% 0.74/1.01 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2263,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[2262])).
% 0.74/1.01 tff(2264,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))))),
% 0.74/1.01 inference(transitivity,[status(thm)],[2263, 2261])).
% 0.74/1.01 tff(2265,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z)))))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(2266,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2265, 2264])).
% 0.74/1.01 tff(2267,plain,
% 0.74/1.01 ((~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(z))))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2266, 206, 2072, 2260])).
% 0.74/1.01 tff(2268,plain,
% 0.74/1.01 (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2267, 2257])).
% 0.74/1.01 tff(2269,plain,
% 0.74/1.01 (r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1213, 150, 1111, 2268])).
% 0.74/1.01 tff(2270,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 0.74/1.01 tff(2271,plain,
% 0.74/1.01 (~r(s(s(s(z))), s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2233, 180, 1313, 2270])).
% 0.74/1.01 tff(2272,plain,
% 0.74/1.01 (b(s(s(s(z))), s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1865, 2271, 1858])).
% 0.74/1.01 tff(2273,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2274,plain,
% 0.74/1.01 (((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2275,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[2274])).
% 0.74/1.01 tff(2276,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.74/1.01 inference(transitivity,[status(thm)],[2275, 2273])).
% 0.74/1.01 tff(2277,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(2278,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2277, 2276])).
% 0.74/1.01 tff(2279,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2278, 206, 1056, 1932, 2272])).
% 0.74/1.01 tff(2280,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (s(s(s(z))) = s(z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(2281,plain,
% 0.74/1.01 (~r(s(s(s(z))), s(s(z)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2280, 2269, 1721, 1564, 2243, 1056])).
% 0.74/1.01 tff(2282,plain,
% 0.74/1.01 (b(s(s(s(z))), s(s(z)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1307, 2281, 2064])).
% 0.74/1.01 tff(2283,plain,
% 0.74/1.01 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1269, 206, 2282, 2063])).
% 0.74/1.01 tff(2284,plain,
% 0.74/1.01 (b(s(s(elem!1)), s(elem!1))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2282, 1897])).
% 0.74/1.01 tff(2285,plain,
% 0.74/1.01 (~b(s(s(elem!1)), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[214, 2284, 2240])).
% 0.74/1.01 tff(2286,plain,
% 0.74/1.01 (r(s(s(elem!1)), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[228, 2285])).
% 0.74/1.01 tff(2287,plain,
% 0.74/1.01 (r(s(s(s(z))), z)),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2286, 1895])).
% 0.74/1.01 tff(2288,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2289,plain,
% 0.74/1.01 (((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2290,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[2289])).
% 0.74/1.01 tff(2291,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 0.74/1.01 inference(transitivity,[status(thm)],[2290, 2288])).
% 0.74/1.01 tff(2292,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(2293,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2292, 2291])).
% 0.74/1.01 tff(2294,plain,
% 0.74/1.01 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2293, 180, 2287, 2246])).
% 0.74/1.01 tff(2295,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1299, 150, 1296, 2294, 2283])).
% 0.74/1.01 tff(2296,plain,((~r(s(elem!1), elem!1)) | (~(elem!1 = s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (elem!1 = z) | (s(elem!1) = s(s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(2297,plain,
% 0.74/1.01 (~r(s(elem!1), elem!1)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2296, 159, 1563, 2062, 135, 18, 58, 2060, 1010])).
% 0.74/1.01 tff(2298,plain,
% 0.74/1.01 (b(s(elem!1), elem!1)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[167, 2297, 38])).
% 0.74/1.01 tff(2299,plain,
% 0.74/1.01 (b(s(s(z)), s(z))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2298, 998])).
% 0.74/1.01 tff(2300,plain,
% 0.74/1.01 (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1209, 206, 2062, 2299])).
% 0.74/1.01 tff(2301,plain,
% 0.74/1.01 (r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1213, 150, 1111, 2300])).
% 0.74/1.01 tff(2302,plain,
% 0.74/1.01 (b(s(s(s(s(z)))), s(s(z)))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2060, 1166])).
% 0.74/1.01 tff(2303,plain,
% 0.74/1.01 (b(s(s(z)), z)),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[95, 2259])).
% 0.74/1.01 tff(2304,plain,
% 0.74/1.01 (~b(z, elem!1)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1188, 95, 1168])).
% 0.74/1.01 tff(2305,plain,
% 0.74/1.01 (r(z, elem!1)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[556, 2304, 109])).
% 0.74/1.01 tff(2306,plain,
% 0.74/1.01 (~r(s(s(s(elem!1))), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[551, 2305, 302])).
% 0.74/1.01 tff(2307,plain,
% 0.74/1.01 (b(s(s(s(elem!1))), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[372, 2306])).
% 0.74/1.01 tff(2308,plain,
% 0.74/1.01 (b(s(s(s(s(z)))), z)),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2307, 1351])).
% 0.74/1.01 tff(2309,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2310,plain,
% 0.74/1.01 (((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2311,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[2310])).
% 0.74/1.01 tff(2312,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.74/1.01 inference(transitivity,[status(thm)],[2311, 2309])).
% 0.74/1.01 tff(2313,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 0.74/1.01 inference(quant_inst,[status(thm)],[])).
% 0.74/1.01 tff(2314,plain,
% 0.74/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(z))))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2313, 2312])).
% 0.74/1.01 tff(2315,plain,
% 0.74/1.01 (~b(s(s(z)), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2314, 206, 1263, 2308])).
% 0.74/1.01 tff(2316,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2315, 2303])).
% 0.74/1.01 tff(2317,plain,((~b(s(elem!1), z)) | (~(elem!1 = s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(elem!1))), elem!1)) | (z = elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(2318,plain,
% 0.74/1.01 (~b(s(elem!1), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2317, 159, 2302, 302, 1011, 2298])).
% 0.74/1.01 tff(2319,plain,
% 0.74/1.01 (r(s(elem!1), z)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[283, 2318])).
% 0.74/1.01 tff(2320,plain,
% 0.74/1.01 (r(s(s(z)), z)),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2319, 1015])).
% 0.74/1.01 tff(2321,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1583, 180, 2320, 1563, 2301])).
% 0.74/1.01 tff(2322,plain,((~(elem!1 = s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (elem!1 = z) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(2323,plain,
% 0.74/1.01 (~r(s(s(s(elem!1))), elem!1)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2322, 982, 994, 58, 11])).
% 0.74/1.01 tff(2324,plain,
% 0.74/1.01 (b(s(s(s(elem!1))), elem!1)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[320, 2323, 58])).
% 0.74/1.01 tff(2325,plain,
% 0.74/1.01 (b(s(s(s(elem!1))), s(z))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2324, 991])).
% 0.74/1.01 tff(2326,assumption,(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))), introduced(assumption)).
% 0.74/1.01 tff(2327,plain,
% 0.74/1.01 (s(s(s(s(s(elem!1))))) = s(s(s(s(z))))),
% 0.74/1.01 inference(transitivity,[status(thm)],[2326, 1003])).
% 0.74/1.01 tff(2328,plain,
% 0.74/1.01 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(z)))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[2327])).
% 0.74/1.01 tff(2329,plain,
% 0.74/1.01 (s(s(s(s(s(z))))) = s(s(s(s(s(s(elem!1))))))),
% 0.74/1.01 inference(symmetry,[status(thm)],[2328])).
% 0.74/1.01 tff(2330,plain,
% 0.74/1.01 (s(s(s(s(s(z))))) = s(s(s(s(elem!1))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[1004])).
% 0.74/1.01 tff(2331,plain,
% 0.74/1.01 (s(s(s(s(elem!1)))) = s(s(s(s(s(z)))))),
% 0.74/1.01 inference(symmetry,[status(thm)],[2330])).
% 0.74/1.01 tff(2332,plain,
% 0.74/1.01 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(z)))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[2327])).
% 0.74/1.01 tff(2333,plain,
% 0.74/1.01 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.74/1.01 inference(symmetry,[status(thm)],[2332])).
% 0.74/1.01 tff(2334,plain,
% 0.74/1.01 (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))),
% 0.74/1.01 inference(transitivity,[status(thm)],[1031, 2333, 1021, 2331, 2329])).
% 0.74/1.01 tff(2335,plain,
% 0.74/1.01 ($false),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[1341, 2334])).
% 0.74/1.01 tff(2336,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.01 tff(2337,plain,
% 0.74/1.01 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2336, 159])).
% 0.74/1.01 tff(2338,plain,
% 0.74/1.01 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[1004])).
% 0.74/1.01 tff(2339,plain,
% 0.74/1.01 ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[2338])).
% 0.74/1.01 tff(2340,plain,
% 0.74/1.01 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 0.74/1.01 inference(monotonicity,[status(thm)],[999])).
% 0.74/1.01 tff(2341,plain,
% 0.74/1.01 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 0.74/1.01 inference(symmetry,[status(thm)],[2340])).
% 0.74/1.01 tff(2342,plain,
% 0.74/1.01 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[1004, 159])).
% 0.74/1.01 tff(2343,plain,
% 0.74/1.01 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 0.74/1.01 inference(symmetry,[status(thm)],[2342])).
% 0.74/1.01 tff(2344,plain,
% 0.74/1.01 (~r(s(s(s(elem!1))), elem!1)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[2322, 159, 994, 58, 11])).
% 0.74/1.01 tff(2345,plain,
% 0.74/1.01 (b(s(s(s(elem!1))), elem!1)),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[320, 2344, 58])).
% 0.74/1.01 tff(2346,plain,
% 0.74/1.01 (b(s(s(s(elem!1))), s(z))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2345, 1736])).
% 0.74/1.01 tff(2347,plain,
% 0.74/1.01 (b(s(s(s(s(z)))), elem!1)),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2346, 2343])).
% 0.74/1.01 tff(2348,plain,
% 0.74/1.01 (b(s(s(s(s(z)))), s(z))),
% 0.74/1.01 inference(modus_ponens,[status(thm)],[2347, 2341])).
% 0.74/1.01 tff(2349,plain,
% 0.74/1.01 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 0.74/1.01 inference(monotonicity,[status(thm)],[159])).
% 0.74/1.01 tff(2350,plain,
% 0.74/1.01 (s(z) = elem!1),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[162, 159])).
% 0.74/1.01 tff(2351,plain,
% 0.74/1.01 (r(z, s(z)) <=> r(z, elem!1)),
% 0.74/1.01 inference(symmetry,[status(thm)],[1902])).
% 0.74/1.01 tff(2352,plain,
% 0.74/1.01 (~b(s(z), s(elem!1))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[907, 899, 2346])).
% 0.74/1.01 tff(2353,plain,
% 0.74/1.01 (r(s(z), s(elem!1))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[467, 2352, 140])).
% 0.74/1.01 tff(2354,plain,
% 0.74/1.01 (~r(s(s(elem!1)), s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[858, 2353, 898])).
% 0.74/1.01 tff(2355,plain,
% 0.74/1.01 (b(s(s(elem!1)), s(z))),
% 0.74/1.01 inference(unit_resolution,[status(thm)],[778, 2354])).
% 0.74/1.01 tff(2356,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2357,plain,
% 0.74/1.01 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 0.74/1.01 inference(rewrite,[status(thm)],[])).
% 0.74/1.01 tff(2358,plain,
% 0.74/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[2357])).
% 0.74/1.02 tff(2359,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))))),
% 0.74/1.02 inference(transitivity,[status(thm)],[2358, 2356])).
% 0.74/1.02 tff(2360,plain,
% 0.74/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(2361,plain,
% 0.74/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z)))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[2360, 2359])).
% 0.74/1.02 tff(2362,plain,
% 0.74/1.02 ($false),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2361, 206, 196, 911, 242])).
% 0.74/1.02 tff(2363,plain,((~b(s(s(elem!1)), s(z))) | (~b(s(s(elem!1)), z)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.74/1.02 tff(2364,plain,
% 0.74/1.02 (~b(z, s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2363, 2355, 196])).
% 0.74/1.02 tff(2365,plain,
% 0.74/1.02 (r(z, s(z))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[505, 2364])).
% 0.74/1.02 tff(2366,plain,
% 0.74/1.02 (r(z, elem!1)),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[2365, 2351])).
% 0.74/1.02 tff(2367,assumption,(~b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 0.74/1.02 tff(2368,assumption,(s(z) = elem!1), introduced(assumption)).
% 0.74/1.02 tff(2369,plain,
% 0.74/1.02 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.74/1.02 inference(monotonicity,[status(thm)],[2368])).
% 0.74/1.02 tff(2370,plain,
% 0.74/1.02 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 0.74/1.02 inference(transitivity,[status(thm)],[2369, 63])).
% 0.74/1.02 tff(2371,plain,
% 0.74/1.02 ((s(s(s(s(s(elem!1))))) = s(z)) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.74/1.02 inference(transitivity,[status(thm)],[2370, 64])).
% 0.74/1.02 tff(2372,plain,
% 0.74/1.02 ((~(s(s(s(s(s(elem!1))))) = s(z))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[2371])).
% 0.74/1.02 tff(2373,plain,
% 0.74/1.02 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[1109, 2372])).
% 0.74/1.02 tff(2374,plain,
% 0.74/1.02 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(2375,plain,
% 0.74/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(2376,plain,
% 0.74/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1)),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[2375, 2374])).
% 0.74/1.02 tff(2377,plain,
% 0.74/1.02 ((s(s(s(s(s(elem!1))))) = elem!1) | b(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(elem!1))))), elem!1)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2376, 150])).
% 0.74/1.02 tff(2378,plain,
% 0.74/1.02 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2377, 2373, 2367])).
% 0.74/1.02 tff(2379,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(2380,plain,
% 0.74/1.02 (((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(2381,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1))))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[2380])).
% 0.74/1.02 tff(2382,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 0.74/1.02 inference(transitivity,[status(thm)],[2381, 2379])).
% 0.74/1.02 tff(2383,plain,
% 0.74/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(2384,plain,
% 0.74/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[2383, 2382])).
% 0.74/1.02 tff(2385,plain,
% 0.74/1.02 (~r(s(s(s(s(s(elem!1))))), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2384, 180, 543, 2378])).
% 0.74/1.02 tff(2386,plain,
% 0.74/1.02 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(2387,plain,
% 0.74/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(2388,plain,
% 0.74/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = z) | b(s(s(s(s(s(elem!1))))), z) | r(s(s(s(s(s(elem!1))))), z)),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[2387, 2386])).
% 0.74/1.02 tff(2389,plain,
% 0.74/1.02 (b(s(s(s(s(s(elem!1))))), z)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2388, 150, 1395, 2385])).
% 0.74/1.02 tff(2390,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(2391,plain,
% 0.74/1.02 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(2392,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[2391])).
% 0.74/1.02 tff(2393,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 0.74/1.02 inference(transitivity,[status(thm)],[2392, 2390])).
% 0.74/1.02 tff(2394,plain,
% 0.74/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(2395,plain,
% 0.74/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[2394, 2393])).
% 0.74/1.02 tff(2396,plain,
% 0.74/1.02 (~b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2395, 206, 95, 2389])).
% 0.74/1.02 tff(2397,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(2398,plain,
% 0.74/1.02 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(2399,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[2398])).
% 0.74/1.02 tff(2400,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 0.74/1.02 inference(transitivity,[status(thm)],[2399, 2397])).
% 0.74/1.02 tff(2401,plain,
% 0.74/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1))))))))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(2402,plain,
% 0.74/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[2401, 2400])).
% 0.74/1.02 tff(2403,plain,
% 0.74/1.02 (~r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2402, 180, 170, 2378])).
% 0.74/1.02 tff(2404,plain,
% 0.74/1.02 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(2405,plain,
% 0.74/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1)))))))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(2406,plain,
% 0.74/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1)))))) | r(s(elem!1), s(s(s(s(s(elem!1))))))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[2405, 2404])).
% 0.74/1.02 tff(2407,plain,
% 0.74/1.02 ((s(elem!1) = s(s(s(s(s(elem!1)))))) | b(s(elem!1), s(s(s(s(s(elem!1))))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2406, 150, 2403])).
% 0.74/1.02 tff(2408,plain,
% 0.74/1.02 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2407, 2396])).
% 0.74/1.02 tff(2409,plain,
% 0.74/1.02 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 0.74/1.02 inference(symmetry,[status(thm)],[2408])).
% 0.74/1.02 tff(2410,plain,
% 0.74/1.02 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(elem!1))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[2409])).
% 0.74/1.02 tff(2411,plain,
% 0.74/1.02 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.74/1.02 inference(symmetry,[status(thm)],[2410])).
% 0.74/1.02 tff(2412,plain,
% 0.74/1.02 (s(z) = s(s(s(s(elem!1))))),
% 0.74/1.02 inference(transitivity,[status(thm)],[2368, 52, 2411, 1021])).
% 0.74/1.02 tff(2413,plain,
% 0.74/1.02 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[2412])).
% 0.74/1.02 tff(2414,plain,
% 0.74/1.02 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 0.74/1.02 inference(symmetry,[status(thm)],[2413])).
% 0.74/1.02 tff(2415,plain,
% 0.74/1.02 (s(s(s(elem!1))) = z),
% 0.74/1.02 inference(transitivity,[status(thm)],[1338, 2414, 106])).
% 0.74/1.02 tff(2416,plain,
% 0.74/1.02 ($false),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[368, 2415])).
% 0.74/1.02 tff(2417,plain,((~(s(z) = elem!1)) | (~b(s(elem!1), z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | b(s(s(s(s(s(elem!1))))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.74/1.02 tff(2418,plain,
% 0.74/1.02 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2417, 2366, 168, 95, 2350])).
% 0.74/1.02 tff(2419,plain,
% 0.74/1.02 (b(s(s(s(s(s(elem!1))))), s(z))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[2418, 2349])).
% 0.74/1.02 tff(2420,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(2421,plain,
% 0.74/1.02 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.74/1.02 inference(rewrite,[status(thm)],[])).
% 0.74/1.02 tff(2422,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 0.74/1.02 inference(monotonicity,[status(thm)],[2421])).
% 0.74/1.02 tff(2423,plain,
% 0.74/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.74/1.02 inference(transitivity,[status(thm)],[2422, 2420])).
% 0.74/1.02 tff(2424,plain,
% 0.74/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.74/1.02 inference(quant_inst,[status(thm)],[])).
% 0.74/1.02 tff(2425,plain,
% 0.74/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[2424, 2423])).
% 0.74/1.02 tff(2426,plain,
% 0.74/1.02 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.74/1.02 inference(unit_resolution,[status(thm)],[2425, 206, 2419, 2348])).
% 0.74/1.02 tff(2427,plain,
% 0.74/1.02 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.74/1.02 inference(modus_ponens,[status(thm)],[2426, 2339])).
% 0.74/1.02 tff(2428,plain,
% 0.74/1.02 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(2429,plain,
% 0.86/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(2430,plain,
% 0.86/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[2429, 2428])).
% 0.86/1.02 tff(2431,plain,
% 0.86/1.02 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[2430, 150])).
% 0.86/1.02 tff(2432,plain,
% 0.86/1.02 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[2431, 2427, 2337])).
% 0.86/1.02 tff(2433,assumption,(s(s(s(z))) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.86/1.02 tff(2434,plain,
% 0.86/1.02 (s(s(s(s(s(elem!1))))) = s(s(s(z)))),
% 0.86/1.02 inference(symmetry,[status(thm)],[2433])).
% 0.86/1.02 tff(2435,plain,
% 0.86/1.02 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(z))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[2434])).
% 0.86/1.02 tff(2436,plain,
% 0.86/1.02 (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))),
% 0.86/1.02 inference(symmetry,[status(thm)],[2435])).
% 0.86/1.02 tff(2437,plain,
% 0.86/1.02 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 0.86/1.02 inference(transitivity,[status(thm)],[1003, 2436])).
% 0.86/1.02 tff(2438,plain,
% 0.86/1.02 ($false),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1053, 2437])).
% 0.86/1.02 tff(2439,plain,((~(s(s(s(z))) = s(s(s(s(s(elem!1))))))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.02 tff(2440,plain,
% 0.86/1.02 (~(s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[2439, 159])).
% 0.86/1.02 tff(2441,plain,
% 0.86/1.02 (r(s(z), s(s(z)))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[2353, 2065])).
% 0.86/1.02 tff(2442,plain,
% 0.86/1.02 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(s(z))), s(s(z)))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[1002, 995])).
% 0.86/1.02 tff(2443,plain,
% 0.86/1.02 (r(s(s(s(z))), s(s(z)))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[898, 2442])).
% 0.86/1.02 tff(2444,plain,
% 0.86/1.02 (~r(s(s(s(z))), s(z))),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[2233, 180, 2443, 2441])).
% 0.86/1.02 tff(2445,plain,
% 0.86/1.02 (b(s(s(s(z))), s(z))),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1865, 2444, 1721])).
% 0.86/1.02 tff(2446,plain,
% 0.86/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(2447,plain,
% 0.86/1.02 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(2448,plain,
% 0.86/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[2447])).
% 0.86/1.02 tff(2449,plain,
% 0.86/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.02 inference(transitivity,[status(thm)],[2448, 2446])).
% 0.86/1.02 tff(2450,plain,
% 0.86/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(2451,plain,
% 0.86/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[2450, 2449])).
% 0.86/1.02 tff(2452,plain,
% 0.86/1.02 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[2451, 206, 2419, 2445])).
% 0.86/1.02 tff(2453,plain,
% 0.86/1.02 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(2454,plain,
% 0.86/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(2455,plain,
% 0.86/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[2454, 2453])).
% 0.86/1.02 tff(2456,plain,
% 0.86/1.02 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[2455, 150, 2452, 2440])).
% 0.86/1.02 tff(2457,plain,
% 0.86/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(2458,plain,
% 0.86/1.02 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(2459,plain,
% 0.86/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[2458])).
% 0.86/1.02 tff(2460,plain,
% 0.86/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.86/1.02 inference(transitivity,[status(thm)],[2459, 2457])).
% 0.86/1.02 tff(2461,plain,
% 0.86/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(2462,plain,
% 0.86/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[2461, 2460])).
% 0.86/1.02 tff(2463,plain,
% 0.86/1.02 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[2462, 206, 2445, 2348])).
% 0.86/1.02 tff(2464,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 0.86/1.02 tff(2465,plain,
% 0.86/1.02 (s(s(s(s(z)))) = s(s(s(z)))),
% 0.86/1.02 inference(symmetry,[status(thm)],[2464])).
% 0.86/1.02 tff(2466,plain,
% 0.86/1.02 ($false),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[1689, 2465])).
% 0.86/1.02 tff(2467,plain,((~(s(s(s(z))) = s(s(s(s(z)))))) | (s(s(s(s(z)))) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.02 tff(2468,plain,
% 0.86/1.02 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[2467, 1296])).
% 0.86/1.02 tff(2469,plain,
% 0.86/1.02 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 0.86/1.02 inference(rewrite,[status(thm)],[])).
% 0.86/1.02 tff(2470,plain,
% 0.86/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z))))))),
% 0.86/1.02 inference(quant_inst,[status(thm)],[])).
% 0.86/1.02 tff(2471,plain,
% 0.86/1.02 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.02 inference(modus_ponens,[status(thm)],[2470, 2469])).
% 0.86/1.02 tff(2472,plain,
% 0.86/1.02 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.02 inference(unit_resolution,[status(thm)],[2471, 150, 2468, 2463])).
% 0.86/1.02 tff(2473,plain,
% 0.86/1.02 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.86/1.02 inference(monotonicity,[status(thm)],[1004])).
% 0.86/1.02 tff(2474,plain,
% 0.86/1.02 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.86/1.02 inference(symmetry,[status(thm)],[2473])).
% 0.86/1.02 tff(2475,assumption,(r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 0.86/1.02 tff(2476,plain,
% 0.86/1.02 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2475, 2474])).
% 0.86/1.03 tff(2477,assumption,(r(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 0.86/1.03 tff(2478,assumption,(r(s(s(s(z))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.86/1.03 tff(2479,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2480,plain,
% 0.86/1.03 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2481,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2480])).
% 0.86/1.03 tff(2482,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2481, 2479])).
% 0.86/1.03 tff(2483,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2484,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2483, 2482])).
% 0.86/1.03 tff(2485,plain,
% 0.86/1.03 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2484, 180, 2478, 2477])).
% 0.86/1.03 tff(2486,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2485, 2476])).
% 0.86/1.03 tff(2487,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~(elem!1 = s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(2488,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2487, 2472, 2456, 2432, 159])).
% 0.86/1.03 tff(2489,plain,((~b(s(s(elem!1)), z)) | (~(elem!1 = s(z))) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = elem!1) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(2490,plain,
% 0.86/1.03 (~b(s(s(elem!1)), z)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2489, 982, 95, 58, 62, 11])).
% 0.86/1.03 tff(2491,plain,
% 0.86/1.03 (r(s(s(elem!1)), z)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[228, 2490])).
% 0.86/1.03 tff(2492,assumption,(~b(s(s(z)), z)), introduced(assumption)).
% 0.86/1.03 tff(2493,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2492, 2303])).
% 0.86/1.03 tff(2494,plain,(b(s(s(z)), z) | (~b(s(elem!1), z)) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(2495,plain,
% 0.86/1.03 (b(s(s(z)), z)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2494, 95, 982])).
% 0.86/1.03 tff(2496,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 0.86/1.03 tff(2497,plain,
% 0.86/1.03 (b(s(z), s(s(z)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[607, 1227])).
% 0.86/1.03 tff(2498,plain,
% 0.86/1.03 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[907, 607, 735])).
% 0.86/1.03 tff(2499,plain,
% 0.86/1.03 (~r(s(s(elem!1)), s(elem!1))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[333, 2498, 58, 62, 11])).
% 0.86/1.03 tff(2500,plain,
% 0.86/1.03 (b(s(s(elem!1)), s(elem!1))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[605, 2499, 57])).
% 0.86/1.03 tff(2501,plain,
% 0.86/1.03 (~b(s(s(elem!1)), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[615, 2500, 607])).
% 0.86/1.03 tff(2502,plain,
% 0.86/1.03 (r(s(s(elem!1)), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[778, 2501])).
% 0.86/1.03 tff(2503,plain,
% 0.86/1.03 (~r(s(z), z)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[789, 2502, 241])).
% 0.86/1.03 tff(2504,plain,
% 0.86/1.03 (b(s(z), z)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[794, 2503])).
% 0.86/1.03 tff(2505,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2506,plain,
% 0.86/1.03 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2507,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2506])).
% 0.86/1.03 tff(2508,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2507, 2505])).
% 0.86/1.03 tff(2509,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2510,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), z))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2509, 2508])).
% 0.86/1.03 tff(2511,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2510, 206, 2504, 2497, 2496])).
% 0.86/1.03 tff(2512,plain,((~b(s(z), s(elem!1))) | (~b(s(s(z)), z)) | (~(elem!1 = s(z))) | (~r(s(s(elem!1)), z)) | (s(s(s(elem!1))) = elem!1) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(2513,plain,
% 0.86/1.03 (~b(s(z), s(elem!1))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2512, 2491, 982, 2495, 58, 62, 11, 2325])).
% 0.86/1.03 tff(2514,plain,
% 0.86/1.03 (r(s(z), s(elem!1))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[467, 2513, 140])).
% 0.86/1.03 tff(2515,plain,
% 0.86/1.03 (r(s(s(z)), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1460, 982, 168])).
% 0.86/1.03 tff(2516,plain,
% 0.86/1.03 (~r(s(z), z)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[789, 781, 241])).
% 0.86/1.03 tff(2517,plain,
% 0.86/1.03 (b(s(z), z)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[794, 2516])).
% 0.86/1.03 tff(2518,plain,
% 0.86/1.03 (~b(s(s(s(elem!1))), z)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[828, 2517, 735])).
% 0.86/1.03 tff(2519,plain,
% 0.86/1.03 (r(s(s(s(elem!1))), z)),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[372, 2518])).
% 0.86/1.03 tff(2520,plain,
% 0.86/1.03 (r(s(s(s(s(z)))), z)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2519, 1471])).
% 0.86/1.03 tff(2521,plain,
% 0.86/1.03 (r(s(s(s(z))), z)),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[241, 1895])).
% 0.86/1.03 tff(2522,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2523,plain,
% 0.86/1.03 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2524,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2523])).
% 0.86/1.03 tff(2525,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2524, 2522])).
% 0.86/1.03 tff(2526,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2527,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2526, 2525])).
% 0.86/1.03 tff(2528,plain,
% 0.86/1.03 ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2527, 180, 2521])).
% 0.86/1.03 tff(2529,plain,
% 0.86/1.03 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2528, 2520])).
% 0.86/1.03 tff(2530,plain,
% 0.86/1.03 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2471, 150, 2529, 2468])).
% 0.86/1.03 tff(2531,plain,
% 0.86/1.03 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 0.86/1.03 inference(symmetry,[status(thm)],[2094])).
% 0.86/1.03 tff(2532,plain,
% 0.86/1.03 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 0.86/1.03 inference(symmetry,[status(thm)],[2093])).
% 0.86/1.03 tff(2533,plain,
% 0.86/1.03 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2091, 2532])).
% 0.86/1.03 tff(2534,plain,
% 0.86/1.03 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2533])).
% 0.86/1.03 tff(2535,plain,
% 0.86/1.03 (~r(s(s(elem!1)), s(elem!1))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[858, 781, 158])).
% 0.86/1.03 tff(2536,plain,
% 0.86/1.03 (b(s(s(elem!1)), s(elem!1))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[605, 2535, 57])).
% 0.86/1.03 tff(2537,plain,
% 0.86/1.03 (b(s(s(s(s(z)))), s(s(s(z)))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[1004, 1012])).
% 0.86/1.03 tff(2538,plain,
% 0.86/1.03 ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2293, 180, 2521])).
% 0.86/1.03 tff(2539,plain,
% 0.86/1.03 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2538, 2520])).
% 0.86/1.03 tff(2540,plain,
% 0.86/1.03 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1299, 150, 1296, 2539])).
% 0.86/1.03 tff(2541,plain,
% 0.86/1.03 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2540, 2537])).
% 0.86/1.03 tff(2542,plain,
% 0.86/1.03 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[640, 2541, 2536])).
% 0.86/1.03 tff(2543,plain,
% 0.86/1.03 (r(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[293, 2542, 11])).
% 0.86/1.03 tff(2544,plain,
% 0.86/1.03 (r(s(s(s(s(z)))), s(s(z)))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2543, 1201])).
% 0.86/1.03 tff(2545,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2546,plain,
% 0.86/1.03 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2547,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2546])).
% 0.86/1.03 tff(2548,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2547, 2545])).
% 0.86/1.03 tff(2549,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2550,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2549, 2548])).
% 0.86/1.03 tff(2551,plain,
% 0.86/1.03 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2550, 180, 2544, 2227])).
% 0.86/1.03 tff(2552,plain,
% 0.86/1.03 (~r(elem!1, s(s(s(elem!1))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2551, 2534])).
% 0.86/1.03 tff(2553,plain,
% 0.86/1.03 (b(elem!1, s(s(s(elem!1))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[533, 2552, 508])).
% 0.86/1.03 tff(2554,plain,
% 0.86/1.03 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2553, 2531])).
% 0.86/1.03 tff(2555,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2556,plain,
% 0.86/1.03 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2557,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2556])).
% 0.86/1.03 tff(2558,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2557, 2555])).
% 0.86/1.03 tff(2559,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2560,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 0.86/1.03 tff(2561,plain,
% 0.86/1.03 (~b(s(s(s(z))), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2560, 206, 2530, 2554])).
% 0.86/1.03 tff(2562,plain,
% 0.86/1.03 (r(s(s(s(z))), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[1865, 2561, 1721])).
% 0.86/1.03 tff(2563,assumption,(~(s(s(s(z))) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.86/1.03 tff(2564,assumption,(b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))), introduced(assumption)).
% 0.86/1.03 tff(2565,assumption,(b(s(z), s(s(s(s(z)))))), introduced(assumption)).
% 0.86/1.03 tff(2566,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2567,plain,
% 0.86/1.03 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2568,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2567])).
% 0.86/1.03 tff(2569,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2568, 2566])).
% 0.86/1.03 tff(2570,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2571,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2570, 2569])).
% 0.86/1.03 tff(2572,plain,
% 0.86/1.03 ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2571, 206, 796, 2565])).
% 0.86/1.03 tff(2573,plain,
% 0.86/1.03 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2572, 2564])).
% 0.86/1.03 tff(2574,plain,
% 0.86/1.03 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z)))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2575,plain,
% 0.86/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z)))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2576,plain,
% 0.86/1.03 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2575, 2574])).
% 0.86/1.03 tff(2577,plain,
% 0.86/1.03 ((s(s(s(s(s(elem!1))))) = s(z)) | b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2576, 150])).
% 0.86/1.03 tff(2578,plain,
% 0.86/1.03 (b(s(s(s(s(s(elem!1))))), s(z)) | r(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2577, 1109])).
% 0.86/1.03 tff(2579,plain,
% 0.86/1.03 (r(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2578, 2573])).
% 0.86/1.03 tff(2580,assumption,(r(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 0.86/1.03 tff(2581,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2582,plain,
% 0.86/1.03 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2583,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 0.86/1.03 inference(monotonicity,[status(thm)],[2582])).
% 0.86/1.03 tff(2584,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.03 inference(transitivity,[status(thm)],[2583, 2581])).
% 0.86/1.03 tff(2585,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.03 inference(quant_inst,[status(thm)],[])).
% 0.86/1.03 tff(2586,plain,
% 0.86/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 0.86/1.03 inference(modus_ponens,[status(thm)],[2585, 2584])).
% 0.86/1.03 tff(2587,plain,
% 0.86/1.03 ($false),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2586, 180, 2580, 2478, 2042])).
% 0.86/1.03 tff(2588,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.03 tff(2589,plain,
% 0.86/1.03 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.03 inference(unit_resolution,[status(thm)],[2588, 2579, 2042])).
% 0.86/1.03 tff(2590,assumption,(b(s(s(s(z))), s(s(s(s(z)))))), introduced(assumption)).
% 0.86/1.03 tff(2591,plain,
% 0.86/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.03 inference(rewrite,[status(thm)],[])).
% 0.86/1.03 tff(2592,plain,
% 0.86/1.03 (((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2593,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2592])).
% 0.86/1.04 tff(2594,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2593, 2591])).
% 0.86/1.04 tff(2595,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2596,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2595, 2594])).
% 0.86/1.04 tff(2597,plain,
% 0.86/1.04 ((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2596, 206, 2590])).
% 0.86/1.04 tff(2598,plain,
% 0.86/1.04 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2597, 2564])).
% 0.86/1.04 tff(2599,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2455, 150, 2598, 2589, 2563])).
% 0.86/1.04 tff(2600,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (s(s(s(z))) = s(s(s(s(s(elem!1)))))) | (~r(s(s(s(z))), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(2601,plain,
% 0.86/1.04 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2600, 2562, 2440, 2517, 2554, 2530])).
% 0.86/1.04 tff(2602,plain,
% 0.86/1.04 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2601, 2339])).
% 0.86/1.04 tff(2603,plain,
% 0.86/1.04 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2431, 2602, 2337])).
% 0.86/1.04 tff(2604,plain,
% 0.86/1.04 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2603, 2474])).
% 0.86/1.04 tff(2605,plain,
% 0.86/1.04 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[995, 1003])).
% 0.86/1.04 tff(2606,plain,
% 0.86/1.04 (b(s(s(z)), s(s(s(s(z))))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 0.86/1.04 inference(symmetry,[status(thm)],[2605])).
% 0.86/1.04 tff(2607,plain,
% 0.86/1.04 ((~b(s(s(z)), s(s(s(s(z)))))) <=> (~b(s(elem!1), s(s(s(elem!1)))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2606])).
% 0.86/1.04 tff(2608,plain,
% 0.86/1.04 (b(s(s(s(s(z)))), elem!1)),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[735, 2343])).
% 0.86/1.04 tff(2609,plain,
% 0.86/1.04 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2608, 2341])).
% 0.86/1.04 tff(2610,plain,
% 0.86/1.04 (b(s(elem!1), s(s(elem!1))) <=> b(s(s(z)), s(s(s(z))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[995, 1002])).
% 0.86/1.04 tff(2611,plain,
% 0.86/1.04 (~(s(elem!1) = s(s(elem!1)))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[680, 57])).
% 0.86/1.04 tff(2612,plain,
% 0.86/1.04 (r(s(s(z)), s(s(s(z)))) <=> r(s(elem!1), s(s(elem!1)))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1070, 1012])).
% 0.86/1.04 tff(2613,plain,
% 0.86/1.04 ((~r(s(s(z)), s(s(s(z))))) <=> (~r(s(elem!1), s(s(elem!1))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2612])).
% 0.86/1.04 tff(2614,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2615,plain,
% 0.86/1.04 (((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2616,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2615])).
% 0.86/1.04 tff(2617,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2616, 2614])).
% 0.86/1.04 tff(2618,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2619,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z)))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2618, 2617])).
% 0.86/1.04 tff(2620,plain,
% 0.86/1.04 (~r(s(s(z)), s(s(s(z))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2619, 180, 2562, 1422])).
% 0.86/1.04 tff(2621,plain,
% 0.86/1.04 (~r(s(elem!1), s(s(elem!1)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2620, 2613])).
% 0.86/1.04 tff(2622,plain,
% 0.86/1.04 (b(s(elem!1), s(s(elem!1)))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[692, 2621, 2611])).
% 0.86/1.04 tff(2623,plain,
% 0.86/1.04 (b(s(s(z)), s(s(s(z))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2622, 2610])).
% 0.86/1.04 tff(2624,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2625,plain,
% 0.86/1.04 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2626,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2625])).
% 0.86/1.04 tff(2627,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2626, 2624])).
% 0.86/1.04 tff(2628,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2629,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), s(z)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2628, 2627])).
% 0.86/1.04 tff(2630,plain,
% 0.86/1.04 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2629, 206, 2623, 2609, 2540])).
% 0.86/1.04 tff(2631,plain,
% 0.86/1.04 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2630, 2607])).
% 0.86/1.04 tff(2632,plain,
% 0.86/1.04 (r(s(elem!1), s(s(s(elem!1))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[354, 2631, 18])).
% 0.86/1.04 tff(2633,plain,
% 0.86/1.04 (r(s(s(z)), s(s(s(s(z)))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2632, 1113])).
% 0.86/1.04 tff(2634,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2635,plain,
% 0.86/1.04 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2636,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2635])).
% 0.86/1.04 tff(2637,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2636, 2634])).
% 0.86/1.04 tff(2638,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2639,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2638, 2637])).
% 0.86/1.04 tff(2640,plain,
% 0.86/1.04 ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2639, 180, 1422, 2633])).
% 0.86/1.04 tff(2641,plain,
% 0.86/1.04 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2640, 2604])).
% 0.86/1.04 tff(2642,plain,
% 0.86/1.04 ((s(s(z)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(z)))),
% 0.86/1.04 inference(commutativity,[status(thm)],[])).
% 0.86/1.04 tff(2643,plain,
% 0.86/1.04 ((~(s(s(z)) = s(s(s(s(s(elem!1))))))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(z))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2642])).
% 0.86/1.04 tff(2644,assumption,(s(s(z)) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.86/1.04 tff(2645,plain,
% 0.86/1.04 (s(s(s(s(s(elem!1))))) = s(s(z))),
% 0.86/1.04 inference(symmetry,[status(thm)],[2644])).
% 0.86/1.04 tff(2646,plain,
% 0.86/1.04 (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2645])).
% 0.86/1.04 tff(2647,plain,
% 0.86/1.04 (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))),
% 0.86/1.04 inference(symmetry,[status(thm)],[2646])).
% 0.86/1.04 tff(2648,plain,
% 0.86/1.04 ($false),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1341, 2647])).
% 0.86/1.04 tff(2649,plain,(~(s(s(z)) = s(s(s(s(s(elem!1))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.04 tff(2650,plain,
% 0.86/1.04 (~(s(s(s(s(s(elem!1))))) = s(s(z)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2649, 2643])).
% 0.86/1.04 tff(2651,plain,
% 0.86/1.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(z))) | b(s(s(s(s(s(elem!1))))), s(s(z))) | r(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(z))) | b(s(s(s(s(s(elem!1))))), s(s(z))) | r(s(s(s(s(s(elem!1))))), s(s(z))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2652,plain,
% 0.86/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(z))) | b(s(s(s(s(s(elem!1))))), s(s(z))) | r(s(s(s(s(s(elem!1))))), s(s(z))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2653,plain,
% 0.86/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(z))) | b(s(s(s(s(s(elem!1))))), s(s(z))) | r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2652, 2651])).
% 0.86/1.04 tff(2654,plain,
% 0.86/1.04 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2653, 150, 2650, 2641])).
% 0.86/1.04 tff(2655,plain,
% 0.86/1.04 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(symmetry,[status(thm)],[1966])).
% 0.86/1.04 tff(2656,plain,
% 0.86/1.04 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(s(s(elem!1)))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[1964])).
% 0.86/1.04 tff(2657,plain,
% 0.86/1.04 (~r(z, s(z))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2050, 2562, 2521])).
% 0.86/1.04 tff(2658,plain,
% 0.86/1.04 (b(z, s(z))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[505, 2657])).
% 0.86/1.04 tff(2659,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2660,plain,
% 0.86/1.04 (((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2661,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2660])).
% 0.86/1.04 tff(2662,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2661, 2659])).
% 0.86/1.04 tff(2663,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2664,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2663, 2662])).
% 0.86/1.04 tff(2665,plain,
% 0.86/1.04 (~b(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2664, 206, 2658, 2609])).
% 0.86/1.04 tff(2666,plain,
% 0.86/1.04 (~b(z, s(s(s(elem!1))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2665, 2656])).
% 0.86/1.04 tff(2667,plain,
% 0.86/1.04 (r(z, s(s(s(elem!1))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[1985, 2666])).
% 0.86/1.04 tff(2668,plain,
% 0.86/1.04 (r(z, s(s(s(s(z)))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2667, 2655])).
% 0.86/1.04 tff(2669,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2670,plain,
% 0.86/1.04 (((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2671,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2670])).
% 0.86/1.04 tff(2672,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2671, 2669])).
% 0.86/1.04 tff(2673,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2674,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2673, 2672])).
% 0.86/1.04 tff(2675,plain,
% 0.86/1.04 ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2674, 180, 2668])).
% 0.86/1.04 tff(2676,plain,
% 0.86/1.04 (~r(s(s(s(s(s(elem!1))))), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2675, 2604])).
% 0.86/1.04 tff(2677,plain,
% 0.86/1.04 (b(s(s(s(s(s(elem!1))))), z)),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2388, 150, 1395, 2676])).
% 0.86/1.04 tff(2678,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2679,plain,
% 0.86/1.04 (((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2680,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 0.86/1.04 inference(monotonicity,[status(thm)],[2679])).
% 0.86/1.04 tff(2681,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.86/1.04 inference(transitivity,[status(thm)],[2680, 2678])).
% 0.86/1.04 tff(2682,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2683,plain,
% 0.86/1.04 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2682, 2681])).
% 0.86/1.04 tff(2684,plain,
% 0.86/1.04 ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2683, 180, 2633])).
% 0.86/1.04 tff(2685,plain,
% 0.86/1.04 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2684, 2604])).
% 0.86/1.04 tff(2686,plain,
% 0.86/1.04 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 0.86/1.04 inference(rewrite,[status(thm)],[])).
% 0.86/1.04 tff(2687,plain,
% 0.86/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 0.86/1.04 inference(quant_inst,[status(thm)],[])).
% 0.86/1.04 tff(2688,plain,
% 0.86/1.04 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(s(elem!1)))))) | b(s(s(z)), s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.86/1.04 inference(modus_ponens,[status(thm)],[2687, 2686])).
% 0.86/1.04 tff(2689,plain,
% 0.86/1.04 (b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.86/1.04 inference(unit_resolution,[status(thm)],[2688, 150, 2685, 2649])).
% 0.86/1.04 tff(2690,plain,
% 0.86/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2691,plain,
% 0.86/1.05 (((~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2692,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2691])).
% 0.86/1.05 tff(2693,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2692, 2690])).
% 0.86/1.05 tff(2694,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2695,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2694, 2693])).
% 0.86/1.05 tff(2696,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2695, 206, 2496, 2689, 2677, 2654])).
% 0.86/1.05 tff(2697,plain,((~r(s(s(elem!1)), s(z))) | (~b(s(s(z)), z)) | (~r(s(s(z)), s(z))) | (~(elem!1 = s(z))) | (elem!1 = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(2698,plain,
% 0.86/1.05 (~r(s(s(elem!1)), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2697, 2495, 2515, 982, 419, 11, 2325, 2514, 2491])).
% 0.86/1.05 tff(2699,plain,
% 0.86/1.05 (b(s(s(elem!1)), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[778, 2698])).
% 0.86/1.05 tff(2700,plain,
% 0.86/1.05 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[759, 2699, 2325])).
% 0.86/1.05 tff(2701,plain,
% 0.86/1.05 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2700, 990])).
% 0.86/1.05 tff(2702,plain,
% 0.86/1.05 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1295, 982])).
% 0.86/1.05 tff(2703,plain,
% 0.86/1.05 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2467, 2702])).
% 0.86/1.05 tff(2704,plain,
% 0.86/1.05 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2471, 150, 2703, 2701])).
% 0.86/1.05 tff(2705,plain,
% 0.86/1.05 (~(s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2439, 982])).
% 0.86/1.05 tff(2706,plain,
% 0.86/1.05 (~(s(s(s(z))) = s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1720, 982])).
% 0.86/1.05 tff(2707,plain,
% 0.86/1.05 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(z))), s(z))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[984])).
% 0.86/1.05 tff(2708,plain,
% 0.86/1.05 ((~r(s(s(elem!1)), s(z))) <=> (~r(s(s(s(z))), s(z)))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2707])).
% 0.86/1.05 tff(2709,plain,
% 0.86/1.05 (~r(s(s(s(z))), s(z))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2698, 2708])).
% 0.86/1.05 tff(2710,plain,
% 0.86/1.05 (b(s(s(s(z))), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[1863, 150, 2709, 2706])).
% 0.86/1.05 tff(2711,plain,
% 0.86/1.05 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[982])).
% 0.86/1.05 tff(2712,plain,
% 0.86/1.05 (s(z) = elem!1),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[162, 982])).
% 0.86/1.05 tff(2713,plain,
% 0.86/1.05 ((s(s(s(z))) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 0.86/1.05 inference(commutativity,[status(thm)],[])).
% 0.86/1.05 tff(2714,plain,
% 0.86/1.05 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(z))) = s(s(s(s(z)))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[984])).
% 0.86/1.05 tff(2715,plain,
% 0.86/1.05 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(s(z))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2714, 2713])).
% 0.86/1.05 tff(2716,plain,
% 0.86/1.05 ((s(s(s(s(z)))) = s(s(s(z)))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 0.86/1.05 inference(symmetry,[status(thm)],[2715])).
% 0.86/1.05 tff(2717,plain,
% 0.86/1.05 ((~(s(s(s(s(z)))) = s(s(s(z))))) <=> (~(s(s(elem!1)) = s(s(s(s(z))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2716])).
% 0.86/1.05 tff(2718,plain,
% 0.86/1.05 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2702, 2717])).
% 0.86/1.05 tff(2719,plain,
% 0.86/1.05 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[986, 982])).
% 0.86/1.05 tff(2720,plain,
% 0.86/1.05 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 0.86/1.05 inference(symmetry,[status(thm)],[2719])).
% 0.86/1.05 tff(2721,plain,
% 0.86/1.05 (b(s(s(s(s(z)))), elem!1)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2325, 2720])).
% 0.86/1.05 tff(2722,plain,
% 0.86/1.05 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[982])).
% 0.86/1.05 tff(2723,plain,
% 0.86/1.05 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 0.86/1.05 inference(symmetry,[status(thm)],[2722])).
% 0.86/1.05 tff(2724,plain,
% 0.86/1.05 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(z))), s(z))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[984])).
% 0.86/1.05 tff(2725,plain,
% 0.86/1.05 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 0.86/1.05 inference(symmetry,[status(thm)],[2724])).
% 0.86/1.05 tff(2726,plain,
% 0.86/1.05 (b(s(s(s(z))), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 0.86/1.05 inference(transitivity,[status(thm)],[2725, 2723])).
% 0.86/1.05 tff(2727,plain,
% 0.86/1.05 (b(s(s(elem!1)), elem!1)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2710, 2726])).
% 0.86/1.05 tff(2728,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 0.86/1.05 tff(2729,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2730,plain,
% 0.86/1.05 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2731,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2730])).
% 0.86/1.05 tff(2732,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2731, 2729])).
% 0.86/1.05 tff(2733,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2734,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2733, 2732])).
% 0.86/1.05 tff(2735,plain,
% 0.86/1.05 (~b(s(s(s(s(z)))), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2734, 206, 797, 2728])).
% 0.86/1.05 tff(2736,plain,
% 0.86/1.05 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2737,plain,
% 0.86/1.05 (~(s(s(s(s(z)))) = z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2736, 222])).
% 0.86/1.05 tff(2738,plain,
% 0.86/1.05 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2739,plain,
% 0.86/1.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2740,plain,
% 0.86/1.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = z) | b(s(s(s(s(z)))), z) | r(s(s(s(s(z)))), z)),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2739, 2738])).
% 0.86/1.05 tff(2741,plain,
% 0.86/1.05 (r(s(s(s(s(z)))), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2740, 150, 2737, 2735])).
% 0.86/1.05 tff(2742,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.86/1.05 tff(2743,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2744,plain,
% 0.86/1.05 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2745,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2744])).
% 0.86/1.05 tff(2746,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2745, 2743])).
% 0.86/1.05 tff(2747,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2748,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2747, 2746])).
% 0.86/1.05 tff(2749,plain,
% 0.86/1.05 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2748, 206, 2742, 2728])).
% 0.86/1.05 tff(2750,assumption,(~(s(s(elem!1)) = s(s(s(s(z)))))), introduced(assumption)).
% 0.86/1.05 tff(2751,plain,
% 0.86/1.05 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2752,plain,
% 0.86/1.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z))))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2753,plain,
% 0.86/1.05 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(z))))) | b(s(s(elem!1)), s(s(s(s(z))))) | r(s(s(elem!1)), s(s(s(s(z)))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2752, 2751])).
% 0.86/1.05 tff(2754,plain,
% 0.86/1.05 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2753, 150, 2750, 2749])).
% 0.86/1.05 tff(2755,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2756,plain,
% 0.86/1.05 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2757,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2756])).
% 0.86/1.05 tff(2758,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2757, 2755])).
% 0.86/1.05 tff(2759,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2760,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2759, 2758])).
% 0.86/1.05 tff(2761,plain,
% 0.86/1.05 (~b(s(s(elem!1)), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2760, 206, 797, 2742])).
% 0.86/1.05 tff(2762,plain,
% 0.86/1.05 (r(s(s(elem!1)), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[228, 2761])).
% 0.86/1.05 tff(2763,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2764,plain,
% 0.86/1.05 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2765,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2764])).
% 0.86/1.05 tff(2766,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2765, 2763])).
% 0.86/1.05 tff(2767,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2768,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2767, 2766])).
% 0.86/1.05 tff(2769,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2768, 180, 2762, 2754, 2741])).
% 0.86/1.05 tff(2770,plain,((~b(s(s(s(s(z)))), elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(2771,plain,
% 0.86/1.05 (~b(z, elem!1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2770, 2727, 2721, 2718])).
% 0.86/1.05 tff(2772,plain,
% 0.86/1.05 (r(z, elem!1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[556, 2771, 993])).
% 0.86/1.05 tff(2773,plain,
% 0.86/1.05 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2417, 2772, 168, 95, 2712])).
% 0.86/1.05 tff(2774,plain,
% 0.86/1.05 (b(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2773, 2711])).
% 0.86/1.05 tff(2775,plain,
% 0.86/1.05 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2451, 206, 2774, 2710])).
% 0.86/1.05 tff(2776,plain,
% 0.86/1.05 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2455, 150, 2775, 2705])).
% 0.86/1.05 tff(2777,plain,
% 0.86/1.05 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2336, 982])).
% 0.86/1.05 tff(2778,plain,
% 0.86/1.05 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[986])).
% 0.86/1.05 tff(2779,plain,
% 0.86/1.05 ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2778])).
% 0.86/1.05 tff(2780,plain,
% 0.86/1.05 (s(z) = elem!1),
% 0.86/1.05 inference(symmetry,[status(thm)],[982])).
% 0.86/1.05 tff(2781,plain,
% 0.86/1.05 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2780])).
% 0.86/1.05 tff(2782,plain,
% 0.86/1.05 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 0.86/1.05 inference(symmetry,[status(thm)],[2781])).
% 0.86/1.05 tff(2783,plain,
% 0.86/1.05 (b(s(s(s(s(z)))), s(z))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2721, 2782])).
% 0.86/1.05 tff(2784,plain,
% 0.86/1.05 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2425, 206, 2774, 2783])).
% 0.86/1.05 tff(2785,plain,
% 0.86/1.05 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2784, 2779])).
% 0.86/1.05 tff(2786,plain,
% 0.86/1.05 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2431, 2785, 2777])).
% 0.86/1.05 tff(2787,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2487, 2786, 2776, 2704, 982])).
% 0.86/1.05 tff(2788,plain,((~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = elem!1) | b(s(elem!1), elem!1) | r(elem!1, s(z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(2789,plain,
% 0.86/1.05 (~b(s(elem!1), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2788, 91, 58, 62, 11])).
% 0.86/1.05 tff(2790,plain,
% 0.86/1.05 (r(s(elem!1), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[283, 2789])).
% 0.86/1.05 tff(2791,plain,
% 0.86/1.05 (~r(elem!1, z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[650, 2790, 168])).
% 0.86/1.05 tff(2792,assumption,(~r(elem!1, z)), introduced(assumption)).
% 0.86/1.05 tff(2793,plain,
% 0.86/1.05 (r(s(s(s(elem!1))), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[733, 728])).
% 0.86/1.05 tff(2794,plain,
% 0.86/1.05 (~(elem!1 = z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[287, 910])).
% 0.86/1.05 tff(2795,plain,
% 0.86/1.05 (b(elem!1, z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[387, 2794, 2792])).
% 0.86/1.05 tff(2796,plain,
% 0.86/1.05 (~r(s(s(elem!1)), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[725, 242, 58, 65, 243, 11, 62, 99])).
% 0.86/1.05 tff(2797,plain,
% 0.86/1.05 (b(s(s(elem!1)), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[228, 2796])).
% 0.86/1.05 tff(2798,plain,
% 0.86/1.05 (~b(z, s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2363, 2797, 242])).
% 0.86/1.05 tff(2799,plain,
% 0.86/1.05 (r(z, s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[505, 2798])).
% 0.86/1.05 tff(2800,plain,
% 0.86/1.05 (~r(s(s(s(elem!1))), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[493, 2799, 243])).
% 0.86/1.05 tff(2801,plain,
% 0.86/1.05 (b(s(s(s(elem!1))), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[372, 2800])).
% 0.86/1.05 tff(2802,plain,
% 0.86/1.05 (~b(s(s(s(elem!1))), elem!1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[662, 2801, 653])).
% 0.86/1.05 tff(2803,plain,
% 0.86/1.05 (r(s(s(s(elem!1))), elem!1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[320, 2802, 58])).
% 0.86/1.05 tff(2804,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2805,plain,
% 0.86/1.05 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2806,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2805])).
% 0.86/1.05 tff(2807,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2806, 2804])).
% 0.86/1.05 tff(2808,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2809,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2808, 2807])).
% 0.86/1.05 tff(2810,plain,
% 0.86/1.05 (~b(elem!1, s(s(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2809, 206, 653, 2797])).
% 0.86/1.05 tff(2811,plain,
% 0.86/1.05 (r(elem!1, s(s(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[889, 2810, 24])).
% 0.86/1.05 tff(2812,plain,
% 0.86/1.05 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[673, 2811, 2803])).
% 0.86/1.05 tff(2813,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2814,plain,
% 0.86/1.05 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.86/1.05 inference(rewrite,[status(thm)],[])).
% 0.86/1.05 tff(2815,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.86/1.05 inference(monotonicity,[status(thm)],[2814])).
% 0.86/1.05 tff(2816,plain,
% 0.86/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.86/1.05 inference(transitivity,[status(thm)],[2815, 2813])).
% 0.86/1.05 tff(2817,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.86/1.05 inference(quant_inst,[status(thm)],[])).
% 0.86/1.05 tff(2818,plain,
% 0.86/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.86/1.05 inference(modus_ponens,[status(thm)],[2817, 2816])).
% 0.86/1.05 tff(2819,plain,
% 0.86/1.05 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2818, 206, 2801, 2797])).
% 0.86/1.05 tff(2820,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[331, 150, 77, 2819, 2812])).
% 0.86/1.05 tff(2821,plain,((~b(s(s(elem!1)), s(z))) | (~b(elem!1, z)) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(s(elem!1))), s(z))) | (elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | b(s(elem!1), elem!1) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(2822,plain,
% 0.86/1.05 (~b(s(s(elem!1)), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2821, 2795, 58, 243, 65, 11, 62, 90])).
% 0.86/1.05 tff(2823,plain,
% 0.86/1.05 (r(s(s(elem!1)), s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[778, 2822])).
% 0.86/1.05 tff(2824,plain,
% 0.86/1.05 (~b(z, s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[957, 196, 11, 62, 65, 58, 157, 243, 59, 910])).
% 0.86/1.05 tff(2825,plain,
% 0.86/1.05 (r(z, s(z))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[505, 2824])).
% 0.86/1.05 tff(2826,plain,
% 0.86/1.05 (~r(s(s(s(elem!1))), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[493, 2825, 243])).
% 0.86/1.05 tff(2827,plain,
% 0.86/1.05 (b(s(s(s(elem!1))), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[372, 2826])).
% 0.86/1.05 tff(2828,plain,
% 0.86/1.05 (~b(s(s(s(elem!1))), elem!1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[662, 2827, 653])).
% 0.86/1.05 tff(2829,plain,
% 0.86/1.05 (r(s(s(s(elem!1))), elem!1)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[320, 2828, 58])).
% 0.86/1.05 tff(2830,plain,
% 0.86/1.05 (~b(elem!1, s(s(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2809, 206, 653, 196])).
% 0.86/1.05 tff(2831,plain,
% 0.86/1.05 (r(elem!1, s(s(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[889, 2830, 24])).
% 0.86/1.05 tff(2832,plain,
% 0.86/1.05 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[673, 2831, 2829])).
% 0.86/1.05 tff(2833,plain,
% 0.86/1.05 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2818, 206, 2827, 196])).
% 0.86/1.05 tff(2834,plain,
% 0.86/1.05 ($false),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[331, 150, 77, 2833, 2832])).
% 0.86/1.05 tff(2835,plain,((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(elem!1), elem!1) | (elem!1 = s(z)) | (~b(elem!1, s(z))) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.05 tff(2836,plain,
% 0.86/1.05 (~b(s(s(elem!1)), z)),
% 0.86/1.05 inference(unit_resolution,[status(thm)],[2835, 2795, 58, 243, 11, 62, 65, 157, 59])).
% 0.86/1.06 tff(2837,plain,
% 0.86/1.06 (r(s(s(elem!1)), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[228, 2836])).
% 0.86/1.06 tff(2838,plain,
% 0.86/1.06 (~r(s(z), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[789, 2837, 2823])).
% 0.86/1.06 tff(2839,plain,
% 0.86/1.06 (b(s(z), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[794, 2838])).
% 0.86/1.06 tff(2840,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2841,plain,
% 0.86/1.06 (((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2842,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), z))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2841])).
% 0.86/1.06 tff(2843,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), z)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2842, 2840])).
% 0.86/1.06 tff(2844,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, s(z))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(2845,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(z), z))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2844, 2843])).
% 0.86/1.06 tff(2846,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2845, 206, 2795, 157, 2839])).
% 0.86/1.06 tff(2847,plain,((s(z) = s(elem!1)) | (~b(elem!1, s(z))) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(elem!1)) | b(s(elem!1), elem!1) | (elem!1 = s(z)) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(2848,plain,
% 0.86/1.06 (s(z) = s(elem!1)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2847, 2793, 58, 157, 11, 62, 65, 2792])).
% 0.86/1.06 tff(2849,plain,
% 0.86/1.06 (b(z, s(z)) <=> b(z, s(elem!1))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2848])).
% 0.86/1.06 tff(2850,plain,
% 0.86/1.06 (b(z, s(elem!1)) <=> b(z, s(z))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2849])).
% 0.86/1.06 tff(2851,plain,
% 0.86/1.06 (s(elem!1) = s(z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[101, 2848])).
% 0.86/1.06 tff(2852,plain,
% 0.86/1.06 (z = elem!1),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[111, 2851])).
% 0.86/1.06 tff(2853,plain,
% 0.86/1.06 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2852])).
% 0.86/1.06 tff(2854,plain,
% 0.86/1.06 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2853])).
% 0.86/1.06 tff(2855,plain,
% 0.86/1.06 (b(elem!1, s(elem!1)) <=> b(z, s(z))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2854, 2850])).
% 0.86/1.06 tff(2856,plain,
% 0.86/1.06 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2848])).
% 0.86/1.06 tff(2857,plain,
% 0.86/1.06 (b(elem!1, s(elem!1))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[157, 2856])).
% 0.86/1.06 tff(2858,plain,
% 0.86/1.06 (b(z, s(z))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2857, 2855])).
% 0.86/1.06 tff(2859,plain,
% 0.86/1.06 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2848])).
% 0.86/1.06 tff(2860,plain,
% 0.86/1.06 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2859])).
% 0.86/1.06 tff(2861,plain,
% 0.86/1.06 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2848])).
% 0.86/1.06 tff(2862,plain,
% 0.86/1.06 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2861])).
% 0.86/1.06 tff(2863,plain,
% 0.86/1.06 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[728, 2862])).
% 0.86/1.06 tff(2864,plain,
% 0.86/1.06 (~r(s(s(elem!1)), s(elem!1))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[333, 2863, 58, 62, 11])).
% 0.86/1.06 tff(2865,plain,
% 0.86/1.06 (b(s(s(elem!1)), s(elem!1))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[605, 2864, 57])).
% 0.86/1.06 tff(2866,plain,
% 0.86/1.06 (b(s(s(elem!1)), s(z))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2865, 2860])).
% 0.86/1.06 tff(2867,plain,
% 0.86/1.06 (~b(s(s(elem!1)), z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2363, 2866, 2858])).
% 0.86/1.06 tff(2868,plain,
% 0.86/1.06 (s(s(elem!1)) = s(s(z))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[86])).
% 0.86/1.06 tff(2869,plain,
% 0.86/1.06 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2868])).
% 0.86/1.06 tff(2870,plain,
% 0.86/1.06 (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1025, 2869])).
% 0.86/1.06 tff(2871,plain,
% 0.86/1.06 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(z))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2870])).
% 0.86/1.06 tff(2872,plain,
% 0.86/1.06 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2871])).
% 0.86/1.06 tff(2873,plain,
% 0.86/1.06 (s(s(z)) = s(s(s(s(s(elem!1)))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1036, 2872, 1023])).
% 0.86/1.06 tff(2874,plain,
% 0.86/1.06 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2873])).
% 0.86/1.06 tff(2875,plain,
% 0.86/1.06 (s(z) = s(s(s(s(elem!1))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1332, 2874, 1021])).
% 0.86/1.06 tff(2876,plain,
% 0.86/1.06 (inj_0(s(z)) = inj_0(s(s(s(s(elem!1)))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2875])).
% 0.86/1.06 tff(2877,plain,
% 0.86/1.06 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2876])).
% 0.86/1.06 tff(2878,plain,
% 0.86/1.06 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2869])).
% 0.86/1.06 tff(2879,plain,
% 0.86/1.06 (s(s(s(z))) = z),
% 0.86/1.06 inference(transitivity,[status(thm)],[2878, 1338, 2877, 106])).
% 0.86/1.06 tff(2880,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[1048, 2879])).
% 0.86/1.06 tff(2881,plain,((~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(2882,plain,
% 0.86/1.06 (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2881, 2851])).
% 0.86/1.06 tff(2883,assumption,(s(s(s(elem!1))) = elem!1), introduced(assumption)).
% 0.86/1.06 tff(2884,plain,
% 0.86/1.06 (s(s(s(s(elem!1)))) = s(elem!1)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2883])).
% 0.86/1.06 tff(2885,plain,
% 0.86/1.06 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2884])).
% 0.86/1.06 tff(2886,plain,
% 0.86/1.06 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2885])).
% 0.86/1.06 tff(2887,plain,
% 0.86/1.06 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 0.86/1.06 inference(transitivity,[status(thm)],[2886, 2883])).
% 0.86/1.06 tff(2888,plain,
% 0.86/1.06 ((elem!1 = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.86/1.06 inference(commutativity,[status(thm)],[])).
% 0.86/1.06 tff(2889,plain,
% 0.86/1.06 ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2883])).
% 0.86/1.06 tff(2890,plain,
% 0.86/1.06 ((s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.86/1.06 inference(transitivity,[status(thm)],[2889, 2888])).
% 0.86/1.06 tff(2891,plain,
% 0.86/1.06 ((~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2890])).
% 0.86/1.06 tff(2892,plain,
% 0.86/1.06 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1606, 2891])).
% 0.86/1.06 tff(2893,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2892, 2887])).
% 0.86/1.06 tff(2894,plain,((~(s(s(s(elem!1))) = elem!1)) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(2895,plain,
% 0.86/1.06 (~(s(s(s(elem!1))) = elem!1)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2894, 1606])).
% 0.86/1.06 tff(2896,plain,
% 0.86/1.06 (s(elem!1) = s(z)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[725, 2793, 242, 241, 2895, 11, 65, 62])).
% 0.86/1.06 tff(2897,plain,
% 0.86/1.06 (z = elem!1),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[111, 2896])).
% 0.86/1.06 tff(2898,plain,
% 0.86/1.06 (b(s(s(s(s(s(s(elem!1)))))), z) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2897])).
% 0.86/1.06 tff(2899,plain,
% 0.86/1.06 (b(s(s(s(s(s(s(elem!1)))))), elem!1) <=> b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.86/1.06 inference(symmetry,[status(thm)],[2898])).
% 0.86/1.06 tff(2900,plain,
% 0.86/1.06 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2897])).
% 0.86/1.06 tff(2901,plain,
% 0.86/1.06 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2900])).
% 0.86/1.06 tff(2902,plain,
% 0.86/1.06 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1557, 2901])).
% 0.86/1.06 tff(2903,plain,
% 0.86/1.06 (s(s(elem!1)) = s(s(z))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2896])).
% 0.86/1.06 tff(2904,plain,
% 0.86/1.06 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2903])).
% 0.86/1.06 tff(2905,plain,
% 0.86/1.06 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2904])).
% 0.86/1.06 tff(2906,plain,
% 0.86/1.06 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2905])).
% 0.86/1.06 tff(2907,plain,
% 0.86/1.06 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2906])).
% 0.86/1.06 tff(2908,plain,
% 0.86/1.06 (r(s(s(s(z))), s(z))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2793, 2907])).
% 0.86/1.06 tff(2909,plain,
% 0.86/1.06 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2896])).
% 0.86/1.06 tff(2910,plain,
% 0.86/1.06 (r(s(z), elem!1)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[253, 2909])).
% 0.86/1.06 tff(2911,plain,
% 0.86/1.06 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2905])).
% 0.86/1.06 tff(2912,plain,
% 0.86/1.06 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 0.86/1.06 inference(symmetry,[status(thm)],[2911])).
% 0.86/1.06 tff(2913,plain,
% 0.86/1.06 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2896])).
% 0.86/1.06 tff(2914,plain,
% 0.86/1.06 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2913])).
% 0.86/1.06 tff(2915,plain,
% 0.86/1.06 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(elem!1))), s(elem!1)))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2914])).
% 0.86/1.06 tff(2916,plain,
% 0.86/1.06 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[728, 2915])).
% 0.86/1.06 tff(2917,plain,
% 0.86/1.06 (~r(s(s(s(elem!1))), elem!1)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[315, 2916, 62, 11])).
% 0.86/1.06 tff(2918,plain,
% 0.86/1.06 (b(s(s(s(elem!1))), elem!1)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[320, 2917, 2895])).
% 0.86/1.06 tff(2919,plain,
% 0.86/1.06 (b(s(s(s(z))), elem!1)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2918, 2912])).
% 0.86/1.06 tff(2920,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 0.86/1.06 tff(2921,plain,
% 0.86/1.06 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.86/1.06 inference(commutativity,[status(thm)],[])).
% 0.86/1.06 tff(2922,plain,
% 0.86/1.06 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2878])).
% 0.86/1.06 tff(2923,plain,
% 0.86/1.06 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2922, 2921])).
% 0.86/1.06 tff(2924,plain,
% 0.86/1.06 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2923])).
% 0.86/1.06 tff(2925,plain,
% 0.86/1.06 ((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(s(s(elem!1)))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2924])).
% 0.86/1.06 tff(2926,plain,
% 0.86/1.06 (z = elem!1),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[111, 86])).
% 0.86/1.06 tff(2927,plain,
% 0.86/1.06 (elem!1 = z),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[137, 2926])).
% 0.86/1.06 tff(2928,plain,
% 0.86/1.06 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(elem!1))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2326])).
% 0.86/1.06 tff(2929,plain,
% 0.86/1.06 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2928])).
% 0.86/1.06 tff(2930,plain,
% 0.86/1.06 (s(s(elem!1)) = s(s(z))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[122])).
% 0.86/1.06 tff(2931,plain,
% 0.86/1.06 (s(s(z)) = s(s(elem!1))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2930])).
% 0.86/1.06 tff(2932,plain,
% 0.86/1.06 (s(s(z)) = s(s(s(s(elem!1))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2931, 72, 2929, 1021])).
% 0.86/1.06 tff(2933,plain,
% 0.86/1.06 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2932])).
% 0.86/1.06 tff(2934,plain,
% 0.86/1.06 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(z)))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2933])).
% 0.86/1.06 tff(2935,plain,
% 0.86/1.06 (s(s(s(elem!1))) = s(z)),
% 0.86/1.06 inference(transitivity,[status(thm)],[1338, 2934, 1018])).
% 0.86/1.06 tff(2936,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[427, 2935])).
% 0.86/1.06 tff(2937,plain,((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) | (~(elem!1 = z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(2938,plain,
% 0.86/1.06 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2937, 2927])).
% 0.86/1.06 tff(2939,plain,
% 0.86/1.06 (~(s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2938, 2925])).
% 0.86/1.06 tff(2940,plain,
% 0.86/1.06 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2588, 2580, 2042])).
% 0.86/1.06 tff(2941,plain,
% 0.86/1.06 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2455, 150, 2940])).
% 0.86/1.06 tff(2942,plain,
% 0.86/1.06 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2941, 2939])).
% 0.86/1.06 tff(2943,plain,
% 0.86/1.06 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2926])).
% 0.86/1.06 tff(2944,plain,
% 0.86/1.06 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2943, 63])).
% 0.86/1.06 tff(2945,plain,
% 0.86/1.06 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.86/1.06 inference(transitivity,[status(thm)],[2944, 64])).
% 0.86/1.06 tff(2946,plain,
% 0.86/1.06 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2945])).
% 0.86/1.06 tff(2947,plain,
% 0.86/1.06 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[1395, 2946])).
% 0.86/1.06 tff(2948,assumption,(r(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 0.86/1.06 tff(2949,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2950,plain,
% 0.86/1.06 (((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2951,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2950])).
% 0.86/1.06 tff(2952,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2951, 2949])).
% 0.86/1.06 tff(2953,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(2954,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2953, 2952])).
% 0.86/1.06 tff(2955,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2954, 180, 169, 2948, 2580])).
% 0.86/1.06 tff(2956,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(2957,plain,
% 0.86/1.06 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2956, 2580, 169])).
% 0.86/1.06 tff(2958,plain,
% 0.86/1.06 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2377, 2957, 2947])).
% 0.86/1.06 tff(2959,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2960,plain,
% 0.86/1.06 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2961,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2960])).
% 0.86/1.06 tff(2962,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2961, 2959])).
% 0.86/1.06 tff(2963,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(2964,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2963, 2962])).
% 0.86/1.06 tff(2965,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2964, 206, 2958, 2942, 2920])).
% 0.86/1.06 tff(2966,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~(s(elem!1) = s(z))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(2967,plain,
% 0.86/1.06 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2966, 2919, 2910, 2896, 2908])).
% 0.86/1.06 tff(2968,plain,
% 0.86/1.06 (b(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2578, 2967])).
% 0.86/1.06 tff(2969,plain,
% 0.86/1.06 (elem!1 = z),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[137, 2897])).
% 0.86/1.06 tff(2970,plain,
% 0.86/1.06 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2937, 2969])).
% 0.86/1.06 tff(2971,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 0.86/1.06 tff(2972,plain,
% 0.86/1.06 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2971])).
% 0.86/1.06 tff(2973,plain,
% 0.86/1.06 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2972])).
% 0.86/1.06 tff(2974,plain,
% 0.86/1.06 (s(s(s(s(elem!1)))) = s(s(s(s(s(elem!1)))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1103, 2973, 1023])).
% 0.86/1.06 tff(2975,plain,
% 0.86/1.06 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2974])).
% 0.86/1.06 tff(2976,plain,
% 0.86/1.06 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(elem!1)))))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2975])).
% 0.86/1.06 tff(2977,plain,
% 0.86/1.06 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2973])).
% 0.86/1.06 tff(2978,plain,
% 0.86/1.06 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.86/1.06 inference(transitivity,[status(thm)],[1096, 2977, 2976, 1337])).
% 0.86/1.06 tff(2979,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), introduced(assumption)).
% 0.86/1.06 tff(2980,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2979, 2978])).
% 0.86/1.06 tff(2981,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(2982,plain,
% 0.86/1.06 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2981, 2970])).
% 0.86/1.06 tff(2983,plain,
% 0.86/1.06 (s(s(z)) = s(s(elem!1))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2903])).
% 0.86/1.06 tff(2984,plain,
% 0.86/1.06 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2983])).
% 0.86/1.06 tff(2985,plain,
% 0.86/1.06 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2984])).
% 0.86/1.06 tff(2986,plain,
% 0.86/1.06 (b(s(s(z)), s(z))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[242, 2985])).
% 0.86/1.06 tff(2987,plain,
% 0.86/1.06 ((s(s(s(s(s(elem!1))))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2642])).
% 0.86/1.06 tff(2988,plain,
% 0.86/1.06 ((~(s(s(s(s(s(elem!1))))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(s(elem!1)))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2987])).
% 0.86/1.06 tff(2989,assumption,(s(s(s(s(s(elem!1))))) = s(s(z))), introduced(assumption)).
% 0.86/1.06 tff(2990,plain,
% 0.86/1.06 (s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2989])).
% 0.86/1.06 tff(2991,plain,
% 0.86/1.06 (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(symmetry,[status(thm)],[2990])).
% 0.86/1.06 tff(2992,plain,
% 0.86/1.06 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[2869, 2991])).
% 0.86/1.06 tff(2993,plain,
% 0.86/1.06 (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2881, 86])).
% 0.86/1.06 tff(2994,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2993, 2992])).
% 0.86/1.06 tff(2995,plain,((~(s(s(s(s(s(elem!1))))) = s(s(z)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(2996,plain,
% 0.86/1.06 (~(s(s(s(s(s(elem!1))))) = s(s(z)))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2995, 2896])).
% 0.86/1.06 tff(2997,plain,
% 0.86/1.06 (~(s(s(z)) = s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[2996, 2988])).
% 0.86/1.06 tff(2998,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(2999,plain,
% 0.86/1.06 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3000,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2999])).
% 0.86/1.06 tff(3001,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[3000, 2998])).
% 0.86/1.06 tff(3002,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(3003,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[3002, 3001])).
% 0.86/1.06 tff(3004,plain,
% 0.86/1.06 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3003, 206, 2968, 2986])).
% 0.86/1.06 tff(3005,plain,
% 0.86/1.06 ((s(s(z)) = s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[2688, 150, 3004])).
% 0.86/1.06 tff(3006,plain,
% 0.86/1.06 (r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3005, 2997])).
% 0.86/1.06 tff(3007,plain,
% 0.86/1.06 (elem!1 = z),
% 0.86/1.06 inference(symmetry,[status(thm)],[2897])).
% 0.86/1.06 tff(3008,plain,
% 0.86/1.06 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[3007])).
% 0.86/1.06 tff(3009,plain,
% 0.86/1.06 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 0.86/1.06 inference(symmetry,[status(thm)],[3008])).
% 0.86/1.06 tff(3010,plain,
% 0.86/1.06 (r(s(s(z)), z) <=> r(s(s(elem!1)), elem!1)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2983, 2897])).
% 0.86/1.06 tff(3011,plain,
% 0.86/1.06 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), z)),
% 0.86/1.06 inference(symmetry,[status(thm)],[3010])).
% 0.86/1.06 tff(3012,plain,
% 0.86/1.06 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 0.86/1.06 inference(monotonicity,[status(thm)],[2897])).
% 0.86/1.06 tff(3013,plain,
% 0.86/1.06 (r(s(s(elem!1)), elem!1)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[241, 3012])).
% 0.86/1.06 tff(3014,plain,
% 0.86/1.06 (r(s(s(z)), z)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[3013, 3011])).
% 0.86/1.06 tff(3015,plain,
% 0.86/1.06 (r(s(s(z)), elem!1)),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[3014, 3009])).
% 0.86/1.06 tff(3016,assumption,(r(s(s(z)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.86/1.06 tff(3017,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 0.86/1.06 tff(3018,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.86/1.06 tff(3019,assumption,(b(s(s(s(s(s(elem!1))))), s(z))), introduced(assumption)).
% 0.86/1.06 tff(3020,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.86/1.06 tff(3021,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3022,plain,
% 0.86/1.06 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3023,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 0.86/1.06 inference(monotonicity,[status(thm)],[3022])).
% 0.86/1.06 tff(3024,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.86/1.06 inference(transitivity,[status(thm)],[3023, 3021])).
% 0.86/1.06 tff(3025,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(3026,plain,
% 0.86/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[3025, 3024])).
% 0.86/1.06 tff(3027,plain,
% 0.86/1.06 ($false),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3026, 206, 3020, 1056, 3019])).
% 0.86/1.06 tff(3028,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.06 tff(3029,plain,
% 0.86/1.06 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3028, 1056, 3019])).
% 0.86/1.06 tff(3030,plain,
% 0.86/1.06 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 0.86/1.06 inference(rewrite,[status(thm)],[])).
% 0.86/1.06 tff(3031,plain,
% 0.86/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 0.86/1.06 inference(quant_inst,[status(thm)],[])).
% 0.86/1.06 tff(3032,plain,
% 0.86/1.06 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(modus_ponens,[status(thm)],[3031, 3030])).
% 0.86/1.06 tff(3033,plain,
% 0.86/1.06 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3032, 150])).
% 0.86/1.06 tff(3034,plain,
% 0.86/1.06 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.86/1.06 inference(unit_resolution,[status(thm)],[3033, 3029, 3018])).
% 0.86/1.06 tff(3035,plain,
% 0.86/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3036,plain,
% 0.86/1.07 (((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3037,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3036])).
% 0.86/1.07 tff(3038,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3037, 3035])).
% 0.86/1.07 tff(3039,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3040,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3039, 3038])).
% 0.86/1.07 tff(3041,plain,
% 0.86/1.07 (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3040, 180, 3034, 3017, 3016])).
% 0.86/1.07 tff(3042,plain,
% 0.86/1.07 (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1209, 206, 1056, 1694])).
% 0.86/1.07 tff(3043,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1213, 150, 1111, 3042, 3041])).
% 0.86/1.07 tff(3044,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(z))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3045,plain,
% 0.86/1.07 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3044, 3015, 3006, 2986, 2982, 2968])).
% 0.86/1.07 tff(3046,plain,
% 0.86/1.07 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1402, 3045])).
% 0.86/1.07 tff(3047,plain,
% 0.86/1.07 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.86/1.07 inference(monotonicity,[status(thm)],[2897])).
% 0.86/1.07 tff(3048,plain,
% 0.86/1.07 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3047, 63])).
% 0.86/1.07 tff(3049,plain,
% 0.86/1.07 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.86/1.07 inference(transitivity,[status(thm)],[3048, 64])).
% 0.86/1.07 tff(3050,plain,
% 0.86/1.07 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3049])).
% 0.86/1.07 tff(3051,plain,
% 0.86/1.07 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[1395, 3050])).
% 0.86/1.07 tff(3052,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3053,plain,
% 0.86/1.07 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3054,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3053])).
% 0.86/1.07 tff(3055,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3054, 3052])).
% 0.86/1.07 tff(3056,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3057,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3056, 3055])).
% 0.86/1.07 tff(3058,plain,
% 0.86/1.07 (~b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3057, 206, 3019, 1694])).
% 0.86/1.07 tff(3059,assumption,(~(s(s(s(s(s(elem!1))))) = s(s(z)))), introduced(assumption)).
% 0.86/1.07 tff(3060,plain,
% 0.86/1.07 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2653, 150, 3059, 3058])).
% 0.86/1.07 tff(3061,assumption,(~(s(s(s(s(s(elem!1))))) = elem!1)), introduced(assumption)).
% 0.86/1.07 tff(3062,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3063,plain,
% 0.86/1.07 (((~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3064,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3063])).
% 0.86/1.07 tff(3065,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3064, 3062])).
% 0.86/1.07 tff(3066,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3067,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3066, 3065])).
% 0.86/1.07 tff(3068,plain,
% 0.86/1.07 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3067, 206, 157, 3019])).
% 0.86/1.07 tff(3069,plain,
% 0.86/1.07 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[2377, 3068, 3061])).
% 0.86/1.07 tff(3070,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3071,plain,
% 0.86/1.07 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3072,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3071])).
% 0.86/1.07 tff(3073,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3072, 3070])).
% 0.86/1.07 tff(3074,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3075,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3074, 3073])).
% 0.86/1.07 tff(3076,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3075, 180, 3069, 3017, 3060])).
% 0.86/1.07 tff(3077,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), elem!1)) | (s(s(s(s(s(elem!1))))) = s(s(z))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3078,plain,
% 0.86/1.07 (~b(elem!1, s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3077, 2968, 2996, 3051, 2986, 3015])).
% 0.86/1.07 tff(3079,plain,
% 0.86/1.07 (r(elem!1, s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[154, 3078, 65])).
% 0.86/1.07 tff(3080,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3081,plain,
% 0.86/1.07 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3082,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3081])).
% 0.86/1.07 tff(3083,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3082, 3080])).
% 0.86/1.07 tff(3084,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3085,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3084, 3083])).
% 0.86/1.07 tff(3086,plain,
% 0.86/1.07 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3085, 180, 3079, 3046])).
% 0.86/1.07 tff(3087,plain,
% 0.86/1.07 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3088,plain,
% 0.86/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3089,plain,
% 0.86/1.07 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3088, 3087])).
% 0.86/1.07 tff(3090,plain,
% 0.86/1.07 ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3089, 150])).
% 0.86/1.07 tff(3091,plain,
% 0.86/1.07 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3090, 3086, 2902])).
% 0.86/1.07 tff(3092,plain,
% 0.86/1.07 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3091, 2899])).
% 0.86/1.07 tff(3093,plain,
% 0.86/1.07 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 0.86/1.07 inference(monotonicity,[status(thm)],[2897])).
% 0.86/1.07 tff(3094,plain,
% 0.86/1.07 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 0.86/1.07 inference(symmetry,[status(thm)],[3093])).
% 0.86/1.07 tff(3095,plain,
% 0.86/1.07 (b(s(s(s(elem!1))), z)),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[2918, 3094])).
% 0.86/1.07 tff(3096,plain,
% 0.86/1.07 (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1413, 3046, 2793])).
% 0.86/1.07 tff(3097,plain,
% 0.86/1.07 (b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1088, 3096, 1606])).
% 0.86/1.07 tff(3098,plain,
% 0.86/1.07 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[1083, 3097, 3095])).
% 0.86/1.07 tff(3099,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3098, 3092])).
% 0.86/1.07 tff(3100,plain,(b(s(s(s(elem!1))), s(z)) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | (elem!1 = s(z)) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3101,plain,
% 0.86/1.07 (~r(s(s(elem!1)), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3100, 2866, 62, 65, 11, 728, 2882])).
% 0.86/1.07 tff(3102,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[228, 3101, 2867])).
% 0.86/1.07 tff(3103,plain,(b(s(s(s(elem!1))), s(z)) | b(s(elem!1), elem!1) | (elem!1 = s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = elem!1) | (~b(elem!1, s(z))) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3104,plain,
% 0.86/1.07 (b(s(s(s(elem!1))), s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3103, 65, 62, 11, 58, 155, 2791])).
% 0.86/1.07 tff(3105,plain,
% 0.86/1.07 (~b(s(s(s(elem!1))), elem!1)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[743, 3104, 155])).
% 0.86/1.07 tff(3106,plain,
% 0.86/1.07 (r(s(s(s(elem!1))), elem!1)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[320, 3105, 58])).
% 0.86/1.07 tff(3107,plain,
% 0.86/1.07 (b(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[315, 3106, 62, 11])).
% 0.86/1.07 tff(3108,plain,
% 0.86/1.07 (~b(s(z), s(elem!1))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[907, 3107, 3104])).
% 0.86/1.07 tff(3109,assumption,(~b(s(z), s(elem!1))), introduced(assumption)).
% 0.86/1.07 tff(3110,plain,
% 0.86/1.07 (~b(s(z), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[828, 357, 735])).
% 0.86/1.07 tff(3111,plain,
% 0.86/1.07 (r(s(z), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[794, 3110])).
% 0.86/1.07 tff(3112,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3113,plain,
% 0.86/1.07 (((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3114,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(z), z))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3113])).
% 0.86/1.07 tff(3115,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3114, 3112])).
% 0.86/1.07 tff(3116,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), elem!1)) | (~r(s(z), s(elem!1))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3117,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(z), z))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3116, 3115])).
% 0.86/1.07 tff(3118,plain,
% 0.86/1.07 (~r(s(z), s(elem!1))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3117, 180, 170, 270, 3111])).
% 0.86/1.07 tff(3119,plain,
% 0.86/1.07 (s(z) = s(elem!1)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[467, 3118, 3109])).
% 0.86/1.07 tff(3120,plain,
% 0.86/1.07 (s(elem!1) = s(z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[101, 3119])).
% 0.86/1.07 tff(3121,plain,
% 0.86/1.07 (z = elem!1),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[111, 3120])).
% 0.86/1.07 tff(3122,plain,
% 0.86/1.07 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3121])).
% 0.86/1.07 tff(3123,plain,
% 0.86/1.07 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 0.86/1.07 inference(symmetry,[status(thm)],[3122])).
% 0.86/1.07 tff(3124,plain,
% 0.86/1.07 ((~r(elem!1, s(elem!1))) <=> (~r(z, s(elem!1)))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3123])).
% 0.86/1.07 tff(3125,plain,
% 0.86/1.07 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3119])).
% 0.86/1.07 tff(3126,plain,
% 0.86/1.07 ((~r(elem!1, s(z))) <=> (~r(elem!1, s(elem!1)))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3125])).
% 0.86/1.07 tff(3127,plain,
% 0.86/1.07 (~r(elem!1, s(elem!1))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[91, 3126])).
% 0.86/1.07 tff(3128,plain,
% 0.86/1.07 (~r(z, s(elem!1))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3127, 3124])).
% 0.86/1.07 tff(3129,plain,
% 0.86/1.07 (r(z, s(z)) <=> r(z, s(elem!1))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3119])).
% 0.86/1.07 tff(3130,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3131,plain,
% 0.86/1.07 (((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3132,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z)))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3131])).
% 0.86/1.07 tff(3133,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3132, 3130])).
% 0.86/1.07 tff(3134,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), z)))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3135,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(z, s(z))) | (~b(s(s(s(elem!1))), s(z)))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3134, 3133])).
% 0.86/1.07 tff(3136,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3135, 206, 357, 911, 735])).
% 0.86/1.07 tff(3137,plain,((~b(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3138,plain,
% 0.86/1.07 (~b(z, s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3137, 357, 735])).
% 0.86/1.07 tff(3139,plain,
% 0.86/1.07 (r(z, s(z))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[505, 3138])).
% 0.86/1.07 tff(3140,plain,
% 0.86/1.07 (r(z, s(elem!1))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3139, 3129])).
% 0.86/1.07 tff(3141,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3140, 3128])).
% 0.86/1.07 tff(3142,plain,((~b(s(s(s(elem!1))), z)) | r(elem!1, s(z)) | b(s(z), s(elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3143,plain,
% 0.86/1.07 (~b(s(s(s(elem!1))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3142, 3108, 91, 168, 2790, 3104])).
% 0.86/1.07 tff(3144,plain,
% 0.86/1.07 (r(s(s(s(elem!1))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[372, 3143])).
% 0.86/1.07 tff(3145,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3146,plain,
% 0.86/1.07 (((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.86/1.07 inference(rewrite,[status(thm)],[])).
% 0.86/1.07 tff(3147,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.86/1.07 inference(monotonicity,[status(thm)],[3146])).
% 0.86/1.07 tff(3148,plain,
% 0.86/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.86/1.07 inference(transitivity,[status(thm)],[3147, 3145])).
% 0.86/1.07 tff(3149,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.86/1.07 inference(quant_inst,[status(thm)],[])).
% 0.86/1.07 tff(3150,plain,
% 0.86/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.86/1.07 inference(modus_ponens,[status(thm)],[3149, 3148])).
% 0.86/1.07 tff(3151,plain,
% 0.86/1.07 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3150, 180, 60, 241])).
% 0.86/1.07 tff(3152,plain,
% 0.86/1.07 (~r(s(s(elem!1)), s(elem!1))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[278, 241, 270])).
% 0.86/1.07 tff(3153,plain,
% 0.86/1.07 (b(s(s(elem!1)), s(elem!1))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[605, 3152, 74])).
% 0.86/1.07 tff(3154,plain,
% 0.86/1.07 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[640, 3153, 61])).
% 0.86/1.07 tff(3155,plain,
% 0.86/1.07 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[76, 74])).
% 0.86/1.07 tff(3156,plain,
% 0.86/1.07 ($false),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[331, 150, 3155, 3154, 3151])).
% 0.86/1.07 tff(3157,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(s(elem!1))), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.07 tff(3158,plain,
% 0.86/1.07 (~r(s(s(elem!1)), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[3157, 3144, 2790, 57, 3107])).
% 0.86/1.07 tff(3159,plain,
% 0.86/1.07 (b(s(s(elem!1)), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[228, 3158])).
% 0.86/1.07 tff(3160,assumption,(~b(s(s(s(elem!1))), z)), introduced(assumption)).
% 0.86/1.07 tff(3161,plain,
% 0.86/1.07 (r(s(s(s(elem!1))), z)),
% 0.86/1.07 inference(unit_resolution,[status(thm)],[372, 3160])).
% 0.86/1.08 tff(3162,plain,
% 0.86/1.08 (~b(s(elem!1), z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[214, 195, 196])).
% 0.86/1.08 tff(3163,plain,
% 0.86/1.08 (r(s(elem!1), z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[283, 3162])).
% 0.86/1.08 tff(3164,plain,
% 0.86/1.08 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[1176, 3163, 3161])).
% 0.86/1.08 tff(3165,plain,
% 0.86/1.08 (b(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[293, 3164, 11])).
% 0.86/1.08 tff(3166,plain,
% 0.86/1.08 (~r(elem!1, z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[650, 3163, 170])).
% 0.86/1.08 tff(3167,plain,
% 0.86/1.08 (~b(s(z), s(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[907, 3165, 735])).
% 0.86/1.08 tff(3168,plain,
% 0.86/1.08 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[640, 3165, 195])).
% 0.86/1.08 tff(3169,plain,
% 0.86/1.08 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[331, 150, 77, 3168])).
% 0.86/1.08 tff(3170,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 0.86/1.08 tff(3171,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3172,plain,
% 0.86/1.08 (((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z))) <=> ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3173,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3172])).
% 0.86/1.08 tff(3174,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3173, 3171])).
% 0.86/1.08 tff(3175,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3176,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), z)) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3175, 3174])).
% 0.86/1.08 tff(3177,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3176, 180, 60, 3170, 643])).
% 0.86/1.08 tff(3178,plain,((~r(z, s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3179,plain,
% 0.86/1.08 (~r(z, s(s(elem!1)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3178, 3169, 3161])).
% 0.86/1.08 tff(3180,plain,
% 0.86/1.08 (b(z, s(s(elem!1)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[2185, 3179])).
% 0.86/1.08 tff(3181,plain,
% 0.86/1.08 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 0.86/1.08 inference(monotonicity,[status(thm)],[133])).
% 0.86/1.08 tff(3182,plain,
% 0.86/1.08 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), z)),
% 0.86/1.08 inference(symmetry,[status(thm)],[3181])).
% 0.86/1.08 tff(3183,plain,
% 0.86/1.08 (b(s(s(s(elem!1))), z)),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[654, 3182])).
% 0.86/1.08 tff(3184,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3160, 3183])).
% 0.86/1.08 tff(3185,plain,((~(z = elem!1)) | b(s(s(s(elem!1))), z) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3186,plain,
% 0.86/1.08 (~(z = elem!1)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3185, 654, 3160])).
% 0.86/1.08 tff(3187,plain,
% 0.86/1.08 (~(s(elem!1) = s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[111, 3186])).
% 0.86/1.08 tff(3188,plain,
% 0.86/1.08 (~(s(z) = s(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[101, 3187])).
% 0.86/1.08 tff(3189,plain,
% 0.86/1.08 (r(s(z), s(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[467, 3188, 3109])).
% 0.86/1.08 tff(3190,plain,
% 0.86/1.08 (~(s(elem!1) = s(s(elem!1)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[680, 874])).
% 0.86/1.08 tff(3191,plain,
% 0.86/1.08 (~(s(s(elem!1)) = elem!1)),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[27, 251])).
% 0.86/1.08 tff(3192,plain,
% 0.86/1.08 (~(elem!1 = z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[287, 3186])).
% 0.86/1.08 tff(3193,plain,
% 0.86/1.08 (b(elem!1, z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[387, 3192, 2792])).
% 0.86/1.08 tff(3194,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3195,plain,
% 0.86/1.08 (((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3196,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3195])).
% 0.86/1.08 tff(3197,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3196, 3194])).
% 0.86/1.08 tff(3198,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3199,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3198, 3197])).
% 0.86/1.08 tff(3200,plain,
% 0.86/1.08 (~b(s(s(elem!1)), elem!1)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3199, 206, 3193, 196])).
% 0.86/1.08 tff(3201,plain,
% 0.86/1.08 ((s(s(elem!1)) = elem!1) | r(s(s(elem!1)), elem!1)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[267, 150, 3200])).
% 0.86/1.08 tff(3202,plain,
% 0.86/1.08 (r(s(s(elem!1)), elem!1)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3201, 3191])).
% 0.86/1.08 tff(3203,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3204,plain,
% 0.86/1.08 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3205,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3204])).
% 0.86/1.08 tff(3206,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3205, 3203])).
% 0.86/1.08 tff(3207,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3208,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3207, 3206])).
% 0.86/1.08 tff(3209,plain,
% 0.86/1.08 (~r(s(elem!1), s(s(elem!1)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3208, 180, 170, 3202])).
% 0.86/1.08 tff(3210,plain,
% 0.86/1.08 (b(s(elem!1), s(s(elem!1)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[692, 3209, 3190])).
% 0.86/1.08 tff(3211,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 0.86/1.08 tff(3212,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3213,plain,
% 0.86/1.08 (((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3214,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3213])).
% 0.86/1.08 tff(3215,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3214, 3212])).
% 0.86/1.08 tff(3216,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3217,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3216, 3215])).
% 0.86/1.08 tff(3218,plain,
% 0.86/1.08 (~b(z, s(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3217, 206, 3211, 3210])).
% 0.86/1.08 tff(3219,plain,
% 0.86/1.08 ((z = s(elem!1)) | r(z, s(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[817, 150, 3218])).
% 0.86/1.08 tff(3220,plain,
% 0.86/1.08 (r(z, s(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3219, 927])).
% 0.86/1.08 tff(3221,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3222,plain,
% 0.86/1.08 (((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), z))) <=> ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3223,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3222])).
% 0.86/1.08 tff(3224,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3223, 3221])).
% 0.86/1.08 tff(3225,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), z)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3226,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), z))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3225, 3224])).
% 0.86/1.08 tff(3227,plain,
% 0.86/1.08 (~r(s(z), z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3226, 180, 3220, 3189])).
% 0.86/1.08 tff(3228,plain,
% 0.86/1.08 (b(s(z), z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[794, 3227])).
% 0.86/1.08 tff(3229,plain,
% 0.86/1.08 (b(elem!1, z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[387, 620, 2792])).
% 0.86/1.08 tff(3230,plain,
% 0.86/1.08 (r(s(z), s(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[467, 244, 3109])).
% 0.86/1.08 tff(3231,plain,
% 0.86/1.08 (~r(elem!1, s(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[450, 3230, 441])).
% 0.86/1.08 tff(3232,plain,
% 0.86/1.08 (b(elem!1, s(elem!1))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[401, 3231, 54])).
% 0.86/1.08 tff(3233,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3234,plain,
% 0.86/1.08 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3235,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3234])).
% 0.86/1.08 tff(3236,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3235, 3233])).
% 0.86/1.08 tff(3237,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3238,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(elem!1, s(elem!1)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3237, 3236])).
% 0.86/1.08 tff(3239,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3238, 206, 3232, 654, 3229, 61])).
% 0.86/1.08 tff(3240,plain,((s(elem!1) = s(z)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (elem!1 = s(elem!1)) | r(elem!1, z) | (~r(elem!1, s(z))) | b(s(z), s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3241,plain,
% 0.86/1.08 (~r(elem!1, s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3240, 3187, 61, 873, 2792, 654, 3109])).
% 0.86/1.08 tff(3242,plain,
% 0.86/1.08 (b(elem!1, s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[154, 3241, 65])).
% 0.86/1.08 tff(3243,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[2845, 206, 3193, 3242, 3228])).
% 0.86/1.08 tff(3244,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), z)) | (elem!1 = s(z)) | b(s(z), s(elem!1)) | r(elem!1, z) | (~b(s(s(s(elem!1))), s(elem!1))) | b(s(s(s(elem!1))), z)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3245,plain,
% 0.86/1.08 (~b(s(s(s(elem!1))), elem!1)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3244, 3180, 170, 24, 196, 65, 3167, 3166, 3165, 3160])).
% 0.86/1.08 tff(3246,plain,
% 0.86/1.08 (r(s(s(s(elem!1))), elem!1)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[320, 3245, 2895])).
% 0.86/1.08 tff(3247,plain,
% 0.86/1.08 (~r(z, elem!1)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[551, 3246, 3161])).
% 0.86/1.08 tff(3248,plain,
% 0.86/1.08 (~r(elem!1, s(s(elem!1)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[673, 3246, 3169])).
% 0.86/1.08 tff(3249,plain,
% 0.86/1.08 (b(elem!1, s(s(elem!1)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[889, 3248, 24])).
% 0.86/1.08 tff(3250,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3251,plain,
% 0.86/1.08 (((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3252,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3251])).
% 0.86/1.08 tff(3253,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3252, 3250])).
% 0.86/1.08 tff(3254,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3255,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(z, s(s(elem!1))))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3254, 3253])).
% 0.86/1.08 tff(3256,plain,
% 0.86/1.08 (~b(z, elem!1)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3255, 206, 3180, 3249])).
% 0.86/1.08 tff(3257,plain,
% 0.86/1.08 (z = elem!1),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[556, 3256, 3247])).
% 0.86/1.08 tff(3258,plain,
% 0.86/1.08 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3257])).
% 0.86/1.08 tff(3259,plain,
% 0.86/1.08 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3258, 63])).
% 0.86/1.08 tff(3260,plain,
% 0.86/1.08 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.86/1.08 inference(transitivity,[status(thm)],[3259, 64])).
% 0.86/1.08 tff(3261,plain,
% 0.86/1.08 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3260])).
% 0.86/1.08 tff(3262,plain,
% 0.86/1.08 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[1395, 3261])).
% 0.86/1.08 tff(3263,plain,
% 0.86/1.08 (s(elem!1) = s(z)),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[239, 3257])).
% 0.86/1.08 tff(3264,plain,
% 0.86/1.08 (s(s(z)) = s(s(elem!1))),
% 0.86/1.08 inference(symmetry,[status(thm)],[2868])).
% 0.86/1.08 tff(3265,plain,
% 0.86/1.08 (elem!1 = z),
% 0.86/1.08 inference(symmetry,[status(thm)],[2926])).
% 0.86/1.08 tff(3266,plain,
% 0.86/1.08 (b(elem!1, s(s(z))) <=> b(z, s(s(elem!1)))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3265, 3264])).
% 0.86/1.08 tff(3267,plain,
% 0.86/1.08 (b(z, s(s(elem!1))) <=> b(elem!1, s(s(z)))),
% 0.86/1.08 inference(symmetry,[status(thm)],[3266])).
% 0.86/1.08 tff(3268,plain,
% 0.86/1.08 (b(elem!1, s(s(z)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3211, 3267])).
% 0.86/1.08 tff(3269,plain,
% 0.86/1.08 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3264, 103])).
% 0.86/1.08 tff(3270,plain,
% 0.86/1.08 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 0.86/1.08 inference(symmetry,[status(thm)],[3269])).
% 0.86/1.08 tff(3271,plain,
% 0.86/1.08 (b(s(s(z)), s(z))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[195, 3270])).
% 0.86/1.08 tff(3272,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3273,plain,
% 0.86/1.08 (((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.86/1.08 inference(rewrite,[status(thm)],[])).
% 0.86/1.08 tff(3274,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3273])).
% 0.86/1.08 tff(3275,plain,
% 0.86/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.86/1.08 inference(transitivity,[status(thm)],[3274, 3272])).
% 0.86/1.08 tff(3276,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 0.86/1.08 inference(quant_inst,[status(thm)],[])).
% 0.86/1.08 tff(3277,plain,
% 0.86/1.08 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[3276, 3275])).
% 0.86/1.08 tff(3278,plain,
% 0.86/1.08 ((~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3277, 206, 157])).
% 0.86/1.08 tff(3279,plain,
% 0.86/1.08 ($false),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3278, 3271, 3268])).
% 0.86/1.08 tff(3280,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(z))) | (~(s(elem!1) = s(z))) | (~b(z, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.08 tff(3281,plain,
% 0.86/1.08 (~b(elem!1, s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[3280, 3263, 3180, 195])).
% 0.86/1.08 tff(3282,plain,
% 0.86/1.08 (r(elem!1, s(z))),
% 0.86/1.08 inference(unit_resolution,[status(thm)],[154, 3281, 65])).
% 0.86/1.08 tff(3283,plain,
% 0.86/1.08 (s(s(elem!1)) = s(s(z))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3263])).
% 0.86/1.08 tff(3284,plain,
% 0.86/1.08 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3283])).
% 0.86/1.08 tff(3285,plain,
% 0.86/1.08 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.86/1.08 inference(symmetry,[status(thm)],[3284])).
% 0.86/1.08 tff(3286,plain,
% 0.86/1.08 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3285])).
% 0.86/1.08 tff(3287,plain,
% 0.86/1.08 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 0.86/1.08 inference(symmetry,[status(thm)],[3286])).
% 0.86/1.08 tff(3288,plain,
% 0.86/1.08 (b(s(s(s(z))), s(z))),
% 0.86/1.08 inference(modus_ponens,[status(thm)],[735, 3287])).
% 0.86/1.08 tff(3289,plain,
% 0.86/1.08 (s(s(z)) = s(s(elem!1))),
% 0.86/1.08 inference(symmetry,[status(thm)],[3283])).
% 0.86/1.08 tff(3290,plain,
% 0.86/1.08 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(z))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3289])).
% 0.86/1.08 tff(3291,plain,
% 0.86/1.08 (b(s(s(elem!1)), s(z)) <=> b(s(s(z)), s(z))),
% 0.86/1.08 inference(symmetry,[status(thm)],[3290])).
% 0.86/1.08 tff(3292,plain,
% 0.86/1.08 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(elem!1)), s(z))),
% 0.86/1.08 inference(monotonicity,[status(thm)],[3263])).
% 0.86/1.09 tff(3293,plain,
% 0.86/1.09 (b(s(s(elem!1)), s(z))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[195, 3292])).
% 0.86/1.09 tff(3294,plain,
% 0.86/1.09 (b(s(s(z)), s(z))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3293, 3291])).
% 0.86/1.09 tff(3295,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3296,plain,
% 0.86/1.09 (((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3297,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3296])).
% 0.86/1.09 tff(3298,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[3297, 3295])).
% 0.86/1.09 tff(3299,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(elem!1, z)))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(3300,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3299, 3298])).
% 0.86/1.09 tff(3301,plain,
% 0.86/1.09 (~b(elem!1, z)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3300, 206, 3180, 3249])).
% 0.86/1.09 tff(3302,plain,
% 0.86/1.09 (elem!1 = z),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[387, 3301, 3166])).
% 0.86/1.09 tff(3303,plain,
% 0.86/1.09 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[2937, 3302])).
% 0.86/1.09 tff(3304,plain,
% 0.86/1.09 (r(s(s(s(z))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3285])).
% 0.86/1.09 tff(3305,plain,
% 0.86/1.09 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(z))), s(s(z)))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3304])).
% 0.86/1.09 tff(3306,plain,
% 0.86/1.09 (r(s(s(s(elem!1))), s(s(elem!1))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3283])).
% 0.86/1.09 tff(3307,plain,
% 0.86/1.09 (r(s(s(s(elem!1))), s(s(z)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3169, 3306])).
% 0.86/1.09 tff(3308,plain,
% 0.86/1.09 (r(s(s(s(z))), s(s(z)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3307, 3305])).
% 0.86/1.09 tff(3309,plain,
% 0.86/1.09 (~(s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[2979, 2925])).
% 0.86/1.09 tff(3310,plain,
% 0.86/1.09 (~(s(s(s(s(s(elem!1))))) = s(s(z)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[2995, 86])).
% 0.86/1.09 tff(3311,plain,
% 0.86/1.09 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[2653, 150, 3310, 3058])).
% 0.86/1.09 tff(3312,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3313,plain,
% 0.86/1.09 (((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3314,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(z))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3313])).
% 0.86/1.09 tff(3315,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[3314, 3312])).
% 0.86/1.09 tff(3316,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(3317,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(z))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3316, 3315])).
% 0.86/1.09 tff(3318,plain,
% 0.86/1.09 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3317, 180, 1313, 3311])).
% 0.86/1.09 tff(3319,plain,
% 0.86/1.09 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[2451, 206, 3019, 1732])).
% 0.86/1.09 tff(3320,plain,
% 0.86/1.09 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[2455, 150, 3319])).
% 0.86/1.09 tff(3321,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3320, 3318, 3309])).
% 0.86/1.09 tff(3322,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~(s(elem!1) = s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3323,plain,
% 0.86/1.09 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3322, 3308, 3303, 3263, 3294, 3288])).
% 0.86/1.09 tff(3324,plain,
% 0.86/1.09 (r(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[2578, 3323])).
% 0.86/1.09 tff(3325,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3326,plain,
% 0.86/1.09 (((~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3327,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3326])).
% 0.86/1.09 tff(3328,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[3327, 3325])).
% 0.86/1.09 tff(3329,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(3330,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3329, 3328])).
% 0.86/1.09 tff(3331,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3330, 180, 441, 2948, 2580])).
% 0.86/1.09 tff(3332,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3333,plain,
% 0.86/1.09 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3332, 3324, 3282])).
% 0.86/1.09 tff(3334,plain,
% 0.86/1.09 (r(s(s(s(s(s(s(elem!1)))))), s(s(z)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1213, 150, 1111, 3042])).
% 0.86/1.09 tff(3335,plain,
% 0.86/1.09 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[2278, 206, 1056, 1732])).
% 0.86/1.09 tff(3336,plain,
% 0.86/1.09 (b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[2878])).
% 0.86/1.09 tff(3337,plain,
% 0.86/1.09 (b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3336])).
% 0.86/1.09 tff(3338,plain,
% 0.86/1.09 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1075, 3337])).
% 0.86/1.09 tff(3339,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1713, 3338])).
% 0.86/1.09 tff(3340,plain,(b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3341,plain,
% 0.86/1.09 (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3340, 3335, 86])).
% 0.86/1.09 tff(3342,plain,
% 0.86/1.09 (r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1088, 3341, 1606])).
% 0.86/1.09 tff(3343,plain,
% 0.86/1.09 (r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[2878])).
% 0.86/1.09 tff(3344,plain,
% 0.86/1.09 (r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3343])).
% 0.86/1.09 tff(3345,plain,
% 0.86/1.09 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1404, 3344])).
% 0.86/1.09 tff(3346,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1712, 3345])).
% 0.86/1.09 tff(3347,plain,(r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3348,plain,
% 0.86/1.09 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3347, 3342, 86])).
% 0.86/1.09 tff(3349,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3350,plain,
% 0.86/1.09 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3351,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3350])).
% 0.86/1.09 tff(3352,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z)))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[3351, 3349])).
% 0.86/1.09 tff(3353,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(3354,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(z))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3353, 3352])).
% 0.86/1.09 tff(3355,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3354, 180, 3348, 1313, 3334])).
% 0.86/1.09 tff(3356,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~(s(elem!1) = s(z))) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3357,plain,
% 0.86/1.09 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3356, 3308, 3263, 1606, 3294, 3288])).
% 0.86/1.09 tff(3358,plain,
% 0.86/1.09 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[1402, 3357])).
% 0.86/1.09 tff(3359,plain,
% 0.86/1.09 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3257])).
% 0.86/1.09 tff(3360,plain,
% 0.86/1.09 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3359])).
% 0.86/1.09 tff(3361,plain,
% 0.86/1.09 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[1557, 3360])).
% 0.86/1.09 tff(3362,plain,
% 0.86/1.09 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[2981, 3303])).
% 0.86/1.09 tff(3363,assumption,(b(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 0.86/1.09 tff(3364,assumption,(~(s(s(s(s(s(s(elem!1)))))) = elem!1)), introduced(assumption)).
% 0.86/1.09 tff(3365,plain,
% 0.86/1.09 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3085, 180, 441, 1405])).
% 0.86/1.09 tff(3366,plain,
% 0.86/1.09 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3090, 3365, 3364])).
% 0.86/1.09 tff(3367,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3368,plain,
% 0.86/1.09 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3369,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3368])).
% 0.86/1.09 tff(3370,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[3369, 3367])).
% 0.86/1.09 tff(3371,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(3372,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3371, 3370])).
% 0.86/1.09 tff(3373,plain,
% 0.86/1.09 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3372, 180, 1405, 2580])).
% 0.86/1.09 tff(3374,plain,
% 0.86/1.09 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3033, 3373, 3018])).
% 0.86/1.09 tff(3375,assumption,(b(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 0.86/1.09 tff(3376,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3377,plain,
% 0.86/1.09 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3378,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3377])).
% 0.86/1.09 tff(3379,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[3378, 3376])).
% 0.86/1.09 tff(3380,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.09 inference(quant_inst,[status(thm)],[])).
% 0.86/1.09 tff(3381,plain,
% 0.86/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3380, 3379])).
% 0.86/1.09 tff(3382,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3381, 206, 3020, 3375, 3363])).
% 0.86/1.09 tff(3383,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3384,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3383, 3374, 3366, 3363])).
% 0.86/1.09 tff(3385,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3386,plain,
% 0.86/1.09 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3385, 3324, 3362, 3361, 3358, 3282])).
% 0.86/1.09 tff(3387,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[2377, 3386, 3333, 3262])).
% 0.86/1.09 tff(3388,plain,((~b(s(s(elem!1)), s(elem!1))) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(z))) | (elem!1 = s(z)) | (~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | b(s(s(s(elem!1))), z) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3389,plain,
% 0.86/1.09 (~b(s(s(elem!1)), s(elem!1))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3388, 735, 1606, 65, 253, 196, 3160, 11])).
% 0.86/1.09 tff(3390,plain,
% 0.86/1.09 (r(s(s(elem!1)), s(elem!1))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[605, 3389, 57])).
% 0.86/1.09 tff(3391,plain,
% 0.86/1.09 (b(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[333, 3390, 2895, 62, 11])).
% 0.86/1.09 tff(3392,plain,
% 0.86/1.09 (~b(s(z), s(elem!1))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[907, 61, 735])).
% 0.86/1.09 tff(3393,plain,
% 0.86/1.09 (r(s(z), s(elem!1))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[467, 244, 3392])).
% 0.86/1.09 tff(3394,plain,
% 0.86/1.09 (~r(s(s(elem!1)), s(z))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[856, 180, 3393, 254])).
% 0.86/1.09 tff(3395,plain,
% 0.86/1.09 (b(s(s(elem!1)), s(z))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[778, 3394])).
% 0.86/1.09 tff(3396,plain,
% 0.86/1.09 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[870, 206, 735, 3395])).
% 0.86/1.09 tff(3397,plain,
% 0.86/1.09 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[331, 150, 521, 3396])).
% 0.86/1.09 tff(3398,plain,
% 0.86/1.09 (~r(z, s(s(elem!1)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3178, 3397, 3161])).
% 0.86/1.09 tff(3399,plain,
% 0.86/1.09 (b(z, s(s(elem!1)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[2185, 3398])).
% 0.86/1.09 tff(3400,plain,
% 0.86/1.09 (~b(elem!1, s(z))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[892, 3395, 58, 196, 517, 735])).
% 0.86/1.09 tff(3401,plain,
% 0.86/1.09 (r(elem!1, s(z))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[154, 3400, 65])).
% 0.86/1.09 tff(3402,plain,
% 0.86/1.09 (~r(elem!1, s(elem!1))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[450, 3401, 3393])).
% 0.86/1.09 tff(3403,plain,
% 0.86/1.09 (b(elem!1, s(elem!1))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[401, 3402, 519])).
% 0.86/1.09 tff(3404,plain,
% 0.86/1.09 (~b(s(elem!1), z)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[396, 3403, 620, 21, 170, 58, 61])).
% 0.86/1.09 tff(3405,plain,
% 0.86/1.09 (r(s(elem!1), z)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[283, 3404])).
% 0.86/1.09 tff(3406,plain,
% 0.86/1.09 (~r(elem!1, z)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[650, 3405, 170])).
% 0.86/1.09 tff(3407,plain,
% 0.86/1.09 (~b(s(s(s(elem!1))), elem!1)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3244, 3406, 170, 517, 196, 65, 3392, 3399, 61, 3160])).
% 0.86/1.09 tff(3408,plain,
% 0.86/1.09 (r(s(s(s(elem!1))), elem!1)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[320, 3407, 58])).
% 0.86/1.09 tff(3409,plain,
% 0.86/1.09 (~r(elem!1, s(s(elem!1)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[673, 3408, 3397])).
% 0.86/1.09 tff(3410,plain,
% 0.86/1.09 (b(elem!1, s(s(elem!1)))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[889, 3409, 517])).
% 0.86/1.09 tff(3411,plain,
% 0.86/1.09 (b(elem!1, z)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[387, 3406, 620])).
% 0.86/1.09 tff(3412,plain,
% 0.86/1.09 ($false),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[2809, 206, 3411, 196, 3410])).
% 0.86/1.09 tff(3413,plain,((s(elem!1) = s(z)) | (~b(s(s(elem!1)), z)) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), elem!1)) | (elem!1 = s(z)) | (~b(s(s(s(elem!1))), s(elem!1))) | b(s(s(s(elem!1))), z) | (s(elem!1) = s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.09 tff(3414,plain,
% 0.86/1.09 (s(elem!1) = s(z)),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[3413, 3391, 2895, 253, 65, 196, 3160, 18, 735, 3390])).
% 0.86/1.09 tff(3415,plain,
% 0.86/1.09 (s(s(elem!1)) = s(s(z))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3414])).
% 0.86/1.09 tff(3416,plain,
% 0.86/1.09 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3415])).
% 0.86/1.09 tff(3417,plain,
% 0.86/1.09 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3416])).
% 0.86/1.09 tff(3418,plain,
% 0.86/1.09 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3417])).
% 0.86/1.09 tff(3419,plain,
% 0.86/1.09 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.86/1.09 inference(transitivity,[status(thm)],[3418, 2921])).
% 0.86/1.09 tff(3420,plain,
% 0.86/1.09 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3419])).
% 0.86/1.09 tff(3421,plain,
% 0.86/1.09 ((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) <=> (~(s(s(s(z))) = s(s(s(s(s(elem!1)))))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3420])).
% 0.86/1.09 tff(3422,plain,
% 0.86/1.09 (z = elem!1),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[111, 3414])).
% 0.86/1.09 tff(3423,plain,
% 0.86/1.09 (elem!1 = z),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[137, 3422])).
% 0.86/1.09 tff(3424,plain,
% 0.86/1.09 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.86/1.09 inference(unit_resolution,[status(thm)],[2937, 3423])).
% 0.86/1.09 tff(3425,plain,
% 0.86/1.09 (~(s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3424, 3421])).
% 0.86/1.09 tff(3426,plain,
% 0.86/1.09 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3417])).
% 0.86/1.09 tff(3427,plain,
% 0.86/1.09 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3426])).
% 0.86/1.09 tff(3428,plain,
% 0.86/1.09 (b(s(s(s(z))), s(z))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[735, 3427])).
% 0.86/1.09 tff(3429,plain,
% 0.86/1.09 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3414])).
% 0.86/1.09 tff(3430,plain,
% 0.86/1.09 (r(s(z), elem!1)),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[253, 3429])).
% 0.86/1.09 tff(3431,plain,
% 0.86/1.09 (s(s(z)) = s(s(elem!1))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3415])).
% 0.86/1.09 tff(3432,plain,
% 0.86/1.09 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(z))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3431])).
% 0.86/1.09 tff(3433,plain,
% 0.86/1.09 (r(s(s(elem!1)), s(z)) <=> r(s(s(z)), s(z))),
% 0.86/1.09 inference(symmetry,[status(thm)],[3432])).
% 0.86/1.09 tff(3434,plain,
% 0.86/1.09 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3414])).
% 0.86/1.09 tff(3435,plain,
% 0.86/1.09 (r(s(s(elem!1)), s(z))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3390, 3434])).
% 0.86/1.09 tff(3436,plain,
% 0.86/1.09 (r(s(s(z)), s(z))),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[3435, 3433])).
% 0.86/1.09 tff(3437,plain,
% 0.86/1.09 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3422])).
% 0.86/1.09 tff(3438,plain,
% 0.86/1.09 (b(s(s(elem!1)), elem!1)),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[196, 3437])).
% 0.86/1.09 tff(3439,plain,
% 0.86/1.09 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3264])).
% 0.86/1.09 tff(3440,plain,
% 0.86/1.09 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 0.86/1.09 inference(symmetry,[status(thm)],[3439])).
% 0.86/1.09 tff(3441,plain,
% 0.86/1.09 (b(s(s(z)), elem!1)),
% 0.86/1.09 inference(modus_ponens,[status(thm)],[2742, 3440])).
% 0.86/1.09 tff(3442,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3443,plain,
% 0.86/1.09 (((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 0.86/1.09 inference(rewrite,[status(thm)],[])).
% 0.86/1.09 tff(3444,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(z)))))),
% 0.86/1.09 inference(monotonicity,[status(thm)],[3443])).
% 0.86/1.09 tff(3445,plain,
% 0.86/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(z))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3444, 3442])).
% 0.86/1.10 tff(3446,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(3447,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(z)))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3446, 3445])).
% 0.86/1.10 tff(3448,plain,
% 0.86/1.10 (~r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3447, 180, 2580, 1422])).
% 0.86/1.10 tff(3449,plain,
% 0.86/1.10 (b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[2653, 150, 3310, 3448])).
% 0.86/1.10 tff(3450,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3451,plain,
% 0.86/1.10 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3452,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3451])).
% 0.86/1.10 tff(3453,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3452, 3450])).
% 0.86/1.10 tff(3454,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(3455,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3454, 3453])).
% 0.86/1.10 tff(3456,plain,
% 0.86/1.10 ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(z))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3455, 206, 2958])).
% 0.86/1.10 tff(3457,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3456, 3449, 3441])).
% 0.86/1.10 tff(3458,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(elem!1)), elem!1)) | (~(s(elem!1) = s(z))) | (~r(s(s(z)), s(z))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(3459,plain,
% 0.86/1.10 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3458, 3438, 3414, 3436, 3430])).
% 0.86/1.10 tff(3460,plain,
% 0.86/1.10 (b(s(s(s(s(s(elem!1))))), s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[2578, 3459])).
% 0.86/1.10 tff(3461,plain,
% 0.86/1.10 (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[2451, 206, 3460, 3428])).
% 0.86/1.10 tff(3462,plain,
% 0.86/1.10 ((s(s(s(z))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[2455, 150, 3461])).
% 0.86/1.10 tff(3463,plain,
% 0.86/1.10 (r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3462, 3425])).
% 0.86/1.10 tff(3464,plain,
% 0.86/1.10 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[2981, 3424])).
% 0.86/1.10 tff(3465,plain,
% 0.86/1.10 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3422])).
% 0.86/1.10 tff(3466,plain,
% 0.86/1.10 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3465, 63])).
% 0.86/1.10 tff(3467,plain,
% 0.86/1.10 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3466])).
% 0.86/1.10 tff(3468,plain,
% 0.86/1.10 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[1395, 3467])).
% 0.86/1.10 tff(3469,plain,
% 0.86/1.10 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3417])).
% 0.86/1.10 tff(3470,plain,
% 0.86/1.10 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 0.86/1.10 inference(symmetry,[status(thm)],[3469])).
% 0.86/1.10 tff(3471,plain,
% 0.86/1.10 (~b(s(s(s(elem!1))), elem!1)),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3185, 3422, 3160])).
% 0.86/1.10 tff(3472,plain,
% 0.86/1.10 (r(s(s(s(elem!1))), elem!1)),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[320, 3471, 2895])).
% 0.86/1.10 tff(3473,plain,
% 0.86/1.10 (r(s(s(s(z))), elem!1)),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3472, 3470])).
% 0.86/1.10 tff(3474,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 0.86/1.10 tff(3475,assumption,(r(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.86/1.10 tff(3476,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3477,plain,
% 0.86/1.10 (((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3478,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3477])).
% 0.86/1.10 tff(3479,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3478, 3476])).
% 0.86/1.10 tff(3480,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(3481,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3480, 3479])).
% 0.86/1.10 tff(3482,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3481, 180, 3475, 2478, 3474])).
% 0.86/1.10 tff(3483,plain,((~r(elem!1, s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(3484,plain,
% 0.86/1.10 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3483, 3463, 3473])).
% 0.86/1.10 tff(3485,plain,
% 0.86/1.10 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1)))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3486,plain,
% 0.86/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1)))))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(3487,plain,
% 0.86/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3486, 3485])).
% 0.86/1.10 tff(3488,plain,
% 0.86/1.10 ((elem!1 = s(s(s(s(s(elem!1)))))) | b(elem!1, s(s(s(s(s(elem!1)))))) | r(elem!1, s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3487, 150])).
% 0.86/1.10 tff(3489,plain,
% 0.86/1.10 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3488, 3484, 3468])).
% 0.86/1.10 tff(3490,assumption,(b(elem!1, s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.86/1.10 tff(3491,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3492,plain,
% 0.86/1.10 (((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3493,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3492])).
% 0.86/1.10 tff(3494,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3493, 3491])).
% 0.86/1.10 tff(3495,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(3496,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3495, 3494])).
% 0.86/1.10 tff(3497,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3496, 206, 157, 3490, 3019])).
% 0.86/1.10 tff(3498,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(3499,plain,
% 0.86/1.10 (~b(elem!1, s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3498, 3489, 3460])).
% 0.86/1.10 tff(3500,plain,
% 0.86/1.10 (r(elem!1, s(z))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[154, 3499, 65])).
% 0.86/1.10 tff(3501,plain,
% 0.86/1.10 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3422])).
% 0.86/1.10 tff(3502,plain,
% 0.86/1.10 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3501])).
% 0.86/1.10 tff(3503,plain,
% 0.86/1.10 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[1557, 3502])).
% 0.86/1.10 tff(3504,plain,
% 0.86/1.10 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3431])).
% 0.86/1.10 tff(3505,plain,
% 0.86/1.10 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 0.86/1.10 inference(symmetry,[status(thm)],[3504])).
% 0.86/1.10 tff(3506,plain,
% 0.86/1.10 (b(s(s(z)), elem!1)),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3438, 3505])).
% 0.86/1.10 tff(3507,plain,
% 0.86/1.10 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 0.86/1.10 inference(symmetry,[status(thm)],[1273])).
% 0.86/1.10 tff(3508,plain,
% 0.86/1.10 ((~(s(s(s(z))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(z)))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3507])).
% 0.86/1.10 tff(3509,assumption,(s(s(s(z))) = s(s(z))), introduced(assumption)).
% 0.86/1.10 tff(3510,plain,
% 0.86/1.10 (s(s(z)) = s(s(s(z)))),
% 0.86/1.10 inference(symmetry,[status(thm)],[3509])).
% 0.86/1.10 tff(3511,plain,
% 0.86/1.10 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3510])).
% 0.86/1.10 tff(3512,plain,
% 0.86/1.10 (inj_0(s(s(s(z)))) = inj_0(s(s(z)))),
% 0.86/1.10 inference(symmetry,[status(thm)],[3511])).
% 0.86/1.10 tff(3513,plain,
% 0.86/1.10 (s(s(elem!1)) = s(z)),
% 0.86/1.10 inference(transitivity,[status(thm)],[2868, 1036, 3512, 1018])).
% 0.86/1.10 tff(3514,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[772, 3513])).
% 0.86/1.10 tff(3515,plain,((~(s(s(s(z))) = s(s(z)))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(3516,plain,
% 0.86/1.10 (~(s(s(s(z))) = s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3515, 3414])).
% 0.86/1.10 tff(3517,plain,
% 0.86/1.10 (~(s(s(z)) = s(s(s(z))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3516, 3508])).
% 0.86/1.10 tff(3518,plain,
% 0.86/1.10 (~(s(s(s(s(s(elem!1))))) = s(s(z)))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[2995, 3414])).
% 0.86/1.10 tff(3519,plain,
% 0.86/1.10 (~(s(s(z)) = s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3518, 2988])).
% 0.86/1.10 tff(3520,plain,
% 0.86/1.10 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.86/1.10 inference(transitivity,[status(thm)],[3466, 64])).
% 0.86/1.10 tff(3521,plain,
% 0.86/1.10 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3520])).
% 0.86/1.10 tff(3522,plain,
% 0.86/1.10 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[1395, 3521])).
% 0.86/1.10 tff(3523,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3524,plain,
% 0.86/1.10 (((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3525,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3524])).
% 0.86/1.10 tff(3526,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3525, 3523])).
% 0.86/1.10 tff(3527,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(3528,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3527, 3526])).
% 0.86/1.10 tff(3529,plain,
% 0.86/1.10 ($false),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3528, 180, 2948, 2478, 3474])).
% 0.86/1.10 tff(3530,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.10 tff(3531,plain,
% 0.86/1.10 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3530, 3463, 3473])).
% 0.86/1.10 tff(3532,plain,
% 0.86/1.10 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[2377, 3531, 3522])).
% 0.86/1.10 tff(3533,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3534,plain,
% 0.86/1.10 (((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3535,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3534])).
% 0.86/1.10 tff(3536,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3535, 3533])).
% 0.86/1.10 tff(3537,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(3538,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3537, 3536])).
% 0.86/1.10 tff(3539,plain,
% 0.86/1.10 ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3538, 206, 3532])).
% 0.86/1.10 tff(3540,plain,
% 0.86/1.10 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3539, 3506])).
% 0.86/1.10 tff(3541,plain,
% 0.86/1.10 ((s(s(z)) = s(s(s(s(s(elem!1)))))) | r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[2688, 150, 3540])).
% 0.86/1.10 tff(3542,plain,
% 0.86/1.10 (r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3541, 3519])).
% 0.86/1.10 tff(3543,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3544,plain,
% 0.86/1.10 (((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3545,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 0.86/1.10 inference(monotonicity,[status(thm)],[3544])).
% 0.86/1.10 tff(3546,plain,
% 0.86/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.10 inference(transitivity,[status(thm)],[3545, 3543])).
% 0.86/1.10 tff(3547,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z))))))),
% 0.86/1.10 inference(quant_inst,[status(thm)],[])).
% 0.86/1.10 tff(3548,plain,
% 0.86/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(z)))))),
% 0.86/1.10 inference(modus_ponens,[status(thm)],[3547, 3546])).
% 0.86/1.10 tff(3549,plain,
% 0.86/1.10 (~r(s(s(z)), s(s(s(z))))),
% 0.86/1.10 inference(unit_resolution,[status(thm)],[3548, 180, 3463, 3542])).
% 0.86/1.10 tff(3550,plain,
% 0.86/1.10 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 0.86/1.10 inference(rewrite,[status(thm)],[])).
% 0.86/1.10 tff(3551,plain,
% 0.86/1.10 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z)))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3552,plain,
% 0.86/1.11 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3551, 3550])).
% 0.86/1.11 tff(3553,plain,
% 0.86/1.11 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3552, 150, 3549])).
% 0.86/1.11 tff(3554,plain,
% 0.86/1.11 (b(s(s(z)), s(s(s(z))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3553, 3517])).
% 0.86/1.11 tff(3555,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 0.86/1.11 tff(3556,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.86/1.11 tff(3557,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3558,plain,
% 0.86/1.11 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3559,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3558])).
% 0.86/1.11 tff(3560,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3559, 3557])).
% 0.86/1.11 tff(3561,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3562,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3561, 3560])).
% 0.86/1.11 tff(3563,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3562, 206, 3366, 3556, 3555, 1434])).
% 0.86/1.11 tff(3564,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3565,plain,
% 0.86/1.11 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3564, 3554, 3506, 3503, 3436, 3500])).
% 0.86/1.11 tff(3566,plain,
% 0.86/1.11 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1402, 3565])).
% 0.86/1.11 tff(3567,plain,
% 0.86/1.11 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3028, 3566, 3460])).
% 0.86/1.11 tff(3568,plain,
% 0.86/1.11 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3033, 3567, 3464])).
% 0.86/1.11 tff(3569,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3570,plain,
% 0.86/1.11 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3571,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3570])).
% 0.86/1.11 tff(3572,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3571, 3569])).
% 0.86/1.11 tff(3573,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3574,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3573, 3572])).
% 0.86/1.11 tff(3575,plain,
% 0.86/1.11 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3574, 180, 3568, 3463])).
% 0.86/1.11 tff(3576,plain,
% 0.86/1.11 (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3347, 3575, 3414])).
% 0.86/1.11 tff(3577,plain,
% 0.86/1.11 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[2278, 206, 3566, 3428])).
% 0.86/1.11 tff(3578,plain,
% 0.86/1.11 (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3340, 3577, 3414])).
% 0.86/1.11 tff(3579,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1088, 3578, 3576, 1606])).
% 0.86/1.11 tff(3580,plain,((~b(s(s(s(elem!1))), s(z))) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | (elem!1 = s(z)) | (~b(s(s(elem!1)), z)) | b(s(s(s(elem!1))), z) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3581,plain,
% 0.86/1.11 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3580, 3159, 62, 65, 3104, 3143, 11])).
% 0.86/1.11 tff(3582,plain,
% 0.86/1.11 (~(s(elem!1) = s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[2881, 3581])).
% 0.86/1.11 tff(3583,plain,
% 0.86/1.11 (~(s(z) = s(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[101, 3582])).
% 0.86/1.11 tff(3584,plain,
% 0.86/1.11 (r(s(z), s(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[467, 3583, 3108])).
% 0.86/1.11 tff(3585,plain,
% 0.86/1.11 (~r(z, elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[551, 3144, 3106])).
% 0.86/1.11 tff(3586,plain,
% 0.86/1.11 (~(z = elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[239, 3582])).
% 0.86/1.11 tff(3587,plain,
% 0.86/1.11 (b(z, elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[556, 3586, 3585])).
% 0.86/1.11 tff(3588,plain,
% 0.86/1.11 (~r(s(z), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[188, 170, 158])).
% 0.86/1.11 tff(3589,plain,
% 0.86/1.11 (b(s(z), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[193, 3588, 156])).
% 0.86/1.11 tff(3590,plain,
% 0.86/1.11 (~b(s(z), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[803, 206, 3589, 797])).
% 0.86/1.11 tff(3591,plain,
% 0.86/1.11 (r(s(z), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[794, 3590])).
% 0.86/1.11 tff(3592,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3117, 180, 170, 270, 3591, 158])).
% 0.86/1.11 tff(3593,plain,((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~b(z, elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3594,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3593, 3587, 3584, 168, 2790, 94])).
% 0.86/1.11 tff(3595,plain,((elem!1 = s(z)) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | r(elem!1, s(z)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3596,plain,
% 0.86/1.11 (elem!1 = s(z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3595, 91, 11, 62, 58])).
% 0.86/1.11 tff(3597,plain,
% 0.86/1.11 (s(elem!1) = s(s(z))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3596])).
% 0.86/1.11 tff(3598,plain,
% 0.86/1.11 (s(s(elem!1)) = s(s(s(z)))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3597])).
% 0.86/1.11 tff(3599,plain,
% 0.86/1.11 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3598])).
% 0.86/1.11 tff(3600,plain,
% 0.86/1.11 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 0.86/1.11 inference(symmetry,[status(thm)],[3599])).
% 0.86/1.11 tff(3601,plain,
% 0.86/1.11 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3600])).
% 0.86/1.11 tff(3602,plain,
% 0.86/1.11 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.86/1.11 inference(symmetry,[status(thm)],[3601])).
% 0.86/1.11 tff(3603,plain,
% 0.86/1.11 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[2336, 3596])).
% 0.86/1.11 tff(3604,plain,
% 0.86/1.11 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3599])).
% 0.86/1.11 tff(3605,plain,
% 0.86/1.11 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.86/1.11 inference(symmetry,[status(thm)],[3604])).
% 0.86/1.11 tff(3606,plain,
% 0.86/1.11 ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3605])).
% 0.86/1.11 tff(3607,plain,
% 0.86/1.11 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(s(z)), s(s(s(s(z)))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3597, 3599])).
% 0.86/1.11 tff(3608,plain,
% 0.86/1.11 (s(s(z)) = s(elem!1)),
% 0.86/1.11 inference(symmetry,[status(thm)],[3597])).
% 0.86/1.11 tff(3609,plain,
% 0.86/1.11 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3608, 3600])).
% 0.86/1.11 tff(3610,plain,
% 0.86/1.11 ((~r(s(s(z)), s(s(s(s(z)))))) <=> (~r(s(elem!1), s(s(s(elem!1)))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3609])).
% 0.86/1.11 tff(3611,plain,
% 0.86/1.11 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3600])).
% 0.86/1.11 tff(3612,plain,
% 0.86/1.11 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 0.86/1.11 inference(symmetry,[status(thm)],[3611])).
% 0.86/1.11 tff(3613,plain,
% 0.86/1.11 ((z = elem!1) <=> (z = s(z))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3596])).
% 0.86/1.11 tff(3614,plain,
% 0.86/1.11 ((z = elem!1) <=> (s(z) = z)),
% 0.86/1.11 inference(transitivity,[status(thm)],[3613, 495])).
% 0.86/1.11 tff(3615,plain,
% 0.86/1.11 ((s(z) = z) <=> (z = elem!1)),
% 0.86/1.11 inference(symmetry,[status(thm)],[3614])).
% 0.86/1.11 tff(3616,plain,
% 0.86/1.11 ((s(z) = z) <=> (elem!1 = z)),
% 0.86/1.11 inference(transitivity,[status(thm)],[3615, 132])).
% 0.86/1.11 tff(3617,plain,
% 0.86/1.11 ((~(s(z) = z)) <=> (~(elem!1 = z))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3616])).
% 0.86/1.11 tff(3618,plain,
% 0.86/1.11 (~(elem!1 = z)),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[499, 3617])).
% 0.86/1.11 tff(3619,plain,
% 0.86/1.11 (b(elem!1, z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[387, 3618, 2791])).
% 0.86/1.11 tff(3620,plain,
% 0.86/1.11 (s(z) = elem!1),
% 0.86/1.11 inference(symmetry,[status(thm)],[3596])).
% 0.86/1.11 tff(3621,plain,
% 0.86/1.11 (b(elem!1, s(z)) <=> b(elem!1, elem!1)),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3620])).
% 0.86/1.11 tff(3622,plain,
% 0.86/1.11 (b(elem!1, elem!1) <=> b(elem!1, s(z))),
% 0.86/1.11 inference(symmetry,[status(thm)],[3621])).
% 0.86/1.11 tff(3623,plain,
% 0.86/1.11 ((~b(elem!1, elem!1)) <=> (~b(elem!1, s(z)))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3622])).
% 0.86/1.11 tff(3624,plain,
% 0.86/1.11 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 0.86/1.11 inference(bind,[status(th)],[])).
% 0.86/1.11 tff(3625,plain,
% 0.86/1.11 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 0.86/1.11 inference(quant_intro,[status(thm)],[3624])).
% 0.86/1.11 tff(3626,plain,
% 0.86/1.11 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3627,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bi')).
% 0.86/1.11 tff(3628,plain,
% 0.86/1.11 (![X: $i] : (~b(X, X))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3627, 3626])).
% 0.86/1.11 tff(3629,plain,(
% 0.86/1.11 ![X: $i] : (~b(X, X))),
% 0.86/1.11 inference(skolemize,[status(sab)],[3628])).
% 0.86/1.11 tff(3630,plain,
% 0.86/1.11 (![X: $i] : (~b(X, X))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3629, 3625])).
% 0.86/1.11 tff(3631,plain,
% 0.86/1.11 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3632,plain,
% 0.86/1.11 (~b(elem!1, elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3631, 3630])).
% 0.86/1.11 tff(3633,plain,
% 0.86/1.11 (~b(elem!1, s(z))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3632, 3623])).
% 0.86/1.11 tff(3634,assumption,(~b(elem!1, s(z))), introduced(assumption)).
% 0.86/1.11 tff(3635,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 0.86/1.11 tff(3636,plain,
% 0.86/1.11 (r(s(s(s(elem!1))), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[320, 58, 3635])).
% 0.86/1.11 tff(3637,plain,
% 0.86/1.11 (~(elem!1 = s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[2322, 3636, 135, 58, 11])).
% 0.86/1.11 tff(3638,plain,
% 0.86/1.11 (r(elem!1, s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[154, 3637, 3634])).
% 0.86/1.11 tff(3639,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3640,plain,
% 0.86/1.11 (((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3641,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3640])).
% 0.86/1.11 tff(3642,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3641, 3639])).
% 0.86/1.11 tff(3643,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3644,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~r(elem!1, s(z)))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3643, 3642])).
% 0.86/1.11 tff(3645,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3644, 180, 302, 441, 243])).
% 0.86/1.11 tff(3646,plain,((~r(s(s(s(elem!1))), s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3647,plain,
% 0.86/1.11 (~r(s(s(s(elem!1))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3646, 302, 441])).
% 0.86/1.11 tff(3648,plain,
% 0.86/1.11 (b(s(s(s(elem!1))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[733, 3647])).
% 0.86/1.11 tff(3649,plain,
% 0.86/1.11 (b(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1192, 60, 302, 1011, 11])).
% 0.86/1.11 tff(3650,plain,
% 0.86/1.11 (~b(s(z), s(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[907, 3649, 3648])).
% 0.86/1.11 tff(3651,plain,
% 0.86/1.11 (r(s(z), s(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[467, 3650, 1469])).
% 0.86/1.11 tff(3652,plain,
% 0.86/1.11 (~r(elem!1, s(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[450, 3651, 441])).
% 0.86/1.11 tff(3653,plain,
% 0.86/1.11 (b(z, elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[556, 1179, 1011])).
% 0.86/1.11 tff(3654,plain,
% 0.86/1.11 (~b(s(elem!1), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1188, 3653, 95])).
% 0.86/1.11 tff(3655,plain,
% 0.86/1.11 (r(s(elem!1), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[167, 3654, 38])).
% 0.86/1.11 tff(3656,plain,
% 0.86/1.11 (~b(elem!1, s(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[396, 3655, 135, 18, 95, 58, 3649])).
% 0.86/1.11 tff(3657,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[401, 3656, 3652, 46])).
% 0.86/1.11 tff(3658,plain,((~r(s(s(s(elem!1))), z)) | (elem!1 = z) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = elem!1) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3659,plain,
% 0.86/1.11 (~r(s(s(s(elem!1))), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3658, 95, 135, 58, 441, 302, 11])).
% 0.86/1.11 tff(3660,plain,
% 0.86/1.11 (b(s(s(s(elem!1))), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[372, 3659])).
% 0.86/1.11 tff(3661,plain,
% 0.86/1.11 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[723, 206, 3660, 95])).
% 0.86/1.11 tff(3662,plain,
% 0.86/1.11 (b(s(elem!1), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[315, 3661, 302, 11])).
% 0.86/1.11 tff(3663,plain,
% 0.86/1.11 (~b(z, s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3137, 3660, 3648])).
% 0.86/1.11 tff(3664,plain,
% 0.86/1.11 (r(z, s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[505, 3663])).
% 0.86/1.11 tff(3665,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3666,plain,
% 0.86/1.11 (((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3667,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3666])).
% 0.86/1.11 tff(3668,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3667, 3665])).
% 0.86/1.11 tff(3669,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, elem!1)))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3670,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3669, 3668])).
% 0.86/1.11 tff(3671,plain,
% 0.86/1.11 (~r(z, elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3670, 180, 441, 3664])).
% 0.86/1.11 tff(3672,plain,
% 0.86/1.11 (b(z, elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[556, 3671, 1011])).
% 0.86/1.11 tff(3673,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[1188, 3672, 3662, 95])).
% 0.86/1.11 tff(3674,plain,((~b(s(elem!1), z)) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(elem!1, s(z))) | (elem!1 = z) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3675,plain,
% 0.86/1.11 (~b(s(elem!1), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3674, 3636, 11, 3638, 135, 58])).
% 0.86/1.11 tff(3676,plain,
% 0.86/1.11 (r(s(elem!1), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[283, 3675])).
% 0.86/1.11 tff(3677,plain,
% 0.86/1.11 (~r(s(s(s(elem!1))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3646, 3636, 3638])).
% 0.86/1.11 tff(3678,plain,
% 0.86/1.11 (b(s(s(s(elem!1))), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[733, 3677])).
% 0.86/1.11 tff(3679,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 0.86/1.11 tff(3680,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3681,plain,
% 0.86/1.11 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3682,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3681])).
% 0.86/1.11 tff(3683,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3682, 3680])).
% 0.86/1.11 tff(3684,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3685,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3684, 3683])).
% 0.86/1.11 tff(3686,plain,
% 0.86/1.11 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3685, 180, 302, 255])).
% 0.86/1.11 tff(3687,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3688,plain,
% 0.86/1.11 (((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3689,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3688])).
% 0.86/1.11 tff(3690,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3689, 3687])).
% 0.86/1.11 tff(3691,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3692,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3691, 3690])).
% 0.86/1.11 tff(3693,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3692, 180, 441, 781, 255])).
% 0.86/1.11 tff(3694,plain,((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3695,plain,
% 0.86/1.11 (~r(s(s(elem!1)), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3694, 255, 441])).
% 0.86/1.11 tff(3696,plain,
% 0.86/1.11 (b(s(s(elem!1)), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[778, 3695])).
% 0.86/1.11 tff(3697,plain,
% 0.86/1.11 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[759, 3696, 3648])).
% 0.86/1.11 tff(3698,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[577, 150, 3697, 3686, 3679])).
% 0.86/1.11 tff(3699,plain,((~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3700,plain,
% 0.86/1.11 (~r(s(s(elem!1)), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3699, 3636, 83, 3638])).
% 0.86/1.11 tff(3701,plain,
% 0.86/1.11 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[267, 150, 3700])).
% 0.86/1.11 tff(3702,plain,
% 0.86/1.11 (b(s(s(elem!1)), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3701, 252])).
% 0.86/1.11 tff(3703,plain,
% 0.86/1.11 (~r(s(s(elem!1)), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3157, 60, 1587, 57, 270])).
% 0.86/1.11 tff(3704,plain,
% 0.86/1.11 (b(s(s(elem!1)), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[228, 3703])).
% 0.86/1.11 tff(3705,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[2760, 206, 797, 2742, 196])).
% 0.86/1.11 tff(3706,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3707,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3706, 3704, 1180, 2742])).
% 0.86/1.11 tff(3708,plain,((~r(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), elem!1)) | (z = elem!1) | (~r(s(elem!1), z)) | (~r(s(s(s(elem!1))), elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3709,plain,
% 0.86/1.11 (~r(s(s(s(elem!1))), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3708, 3702, 1011, 3676, 3636, 11])).
% 0.86/1.11 tff(3710,plain,
% 0.86/1.11 (b(s(s(s(elem!1))), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[372, 3709])).
% 0.86/1.11 tff(3711,plain,
% 0.86/1.11 (~b(s(z), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[828, 3710, 3678])).
% 0.86/1.11 tff(3712,plain,
% 0.86/1.11 (r(s(z), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[794, 3711])).
% 0.86/1.11 tff(3713,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3714,plain,
% 0.86/1.11 (((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 0.86/1.11 inference(rewrite,[status(thm)],[])).
% 0.86/1.11 tff(3715,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(z), z))))),
% 0.86/1.11 inference(monotonicity,[status(thm)],[3714])).
% 0.86/1.11 tff(3716,plain,
% 0.86/1.11 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(z), z)))),
% 0.86/1.11 inference(transitivity,[status(thm)],[3715, 3713])).
% 0.86/1.11 tff(3717,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))))),
% 0.86/1.11 inference(quant_inst,[status(thm)],[])).
% 0.86/1.11 tff(3718,plain,
% 0.86/1.11 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(z), s(elem!1))) | (~r(s(z), z))),
% 0.86/1.11 inference(modus_ponens,[status(thm)],[3717, 3716])).
% 0.86/1.11 tff(3719,plain,
% 0.86/1.11 (~r(s(z), s(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3718, 180, 3676, 3712])).
% 0.86/1.11 tff(3720,plain,
% 0.86/1.11 (b(s(z), s(elem!1))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[467, 3719, 1469])).
% 0.86/1.11 tff(3721,plain,
% 0.86/1.11 (~b(s(s(elem!1)), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[615, 3153, 607])).
% 0.86/1.11 tff(3722,plain,
% 0.86/1.11 (r(s(s(elem!1)), s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[778, 3721])).
% 0.86/1.11 tff(3723,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[787, 180, 3722, 780, 241])).
% 0.86/1.11 tff(3724,plain,((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~b(s(z), s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3725,plain,
% 0.86/1.11 (~r(s(s(elem!1)), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3724, 3720, 3712, 57, 3676])).
% 0.86/1.11 tff(3726,plain,
% 0.86/1.11 (~b(z, s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3137, 3710, 3678])).
% 0.86/1.11 tff(3727,plain,
% 0.86/1.11 (r(z, s(z))),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[505, 3726])).
% 0.86/1.11 tff(3728,plain,
% 0.86/1.11 (~r(z, elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3670, 180, 3638, 3727])).
% 0.86/1.11 tff(3729,plain,
% 0.86/1.11 (b(z, elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[556, 3728, 1011])).
% 0.86/1.11 tff(3730,plain,
% 0.86/1.11 (~b(s(s(elem!1)), z)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3706, 3729, 3702])).
% 0.86/1.11 tff(3731,plain,
% 0.86/1.11 ($false),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[228, 3730, 3725])).
% 0.86/1.11 tff(3732,plain,((s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (elem!1 = z) | b(elem!1, s(z)) | b(s(s(s(elem!1))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.86/1.11 tff(3733,plain,
% 0.86/1.11 (b(s(s(s(elem!1))), elem!1)),
% 0.86/1.11 inference(unit_resolution,[status(thm)],[3732, 3633, 58, 3618, 11])).
% 0.86/1.11 tff(3734,plain,
% 0.86/1.12 (~b(s(s(s(elem!1))), z)),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[662, 3733, 3619])).
% 0.86/1.12 tff(3735,plain,
% 0.86/1.12 (r(s(s(s(elem!1))), z)),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[372, 3734])).
% 0.86/1.12 tff(3736,plain,
% 0.86/1.12 (r(s(s(s(s(z)))), z)),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3735, 3612])).
% 0.86/1.12 tff(3737,plain,
% 0.86/1.12 (r(s(elem!1), z) <=> r(s(s(z)), z)),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3597])).
% 0.86/1.12 tff(3738,plain,
% 0.86/1.12 (r(s(s(z)), z)),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[2790, 3737])).
% 0.86/1.12 tff(3739,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(3740,plain,
% 0.86/1.12 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(3741,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3740])).
% 0.86/1.12 tff(3742,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.86/1.12 inference(transitivity,[status(thm)],[3741, 3739])).
% 0.86/1.12 tff(3743,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(3744,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3743, 3742])).
% 0.86/1.12 tff(3745,plain,
% 0.86/1.12 ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3744, 180, 3738])).
% 0.86/1.12 tff(3746,plain,
% 0.86/1.12 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3745, 3736])).
% 0.86/1.12 tff(3747,plain,
% 0.86/1.12 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3746, 3610])).
% 0.86/1.12 tff(3748,plain,
% 0.86/1.12 (b(s(elem!1), s(s(s(elem!1))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[354, 3747, 18])).
% 0.86/1.12 tff(3749,plain,
% 0.86/1.12 (b(s(s(z)), s(s(s(s(z)))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3748, 3607])).
% 0.86/1.12 tff(3750,plain,
% 0.86/1.12 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3596, 3599])).
% 0.86/1.12 tff(3751,plain,
% 0.86/1.12 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3596])).
% 0.86/1.12 tff(3752,plain,
% 0.86/1.12 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
% 0.86/1.12 inference(symmetry,[status(thm)],[3751])).
% 0.86/1.12 tff(3753,plain,
% 0.86/1.12 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(elem!1))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3600])).
% 0.86/1.12 tff(3754,plain,
% 0.86/1.12 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[3753, 3752])).
% 0.86/1.12 tff(3755,plain,
% 0.86/1.12 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3754])).
% 0.86/1.12 tff(3756,plain,
% 0.86/1.12 (s(s(s(z))) = s(s(elem!1))),
% 0.86/1.12 inference(symmetry,[status(thm)],[3598])).
% 0.86/1.12 tff(3757,plain,
% 0.86/1.12 (r(s(z), s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3620, 3756])).
% 0.86/1.12 tff(3758,plain,
% 0.86/1.12 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(s(z))))),
% 0.86/1.12 inference(symmetry,[status(thm)],[3757])).
% 0.86/1.12 tff(3759,plain,
% 0.86/1.12 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(z))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3598])).
% 0.86/1.12 tff(3760,plain,
% 0.86/1.12 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 0.86/1.12 inference(symmetry,[status(thm)],[3759])).
% 0.86/1.12 tff(3761,plain,
% 0.86/1.12 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3620])).
% 0.86/1.12 tff(3762,plain,
% 0.86/1.12 (b(s(z), s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 0.86/1.12 inference(transitivity,[status(thm)],[3761, 3760])).
% 0.86/1.12 tff(3763,plain,
% 0.86/1.12 ((~b(s(z), s(s(s(z))))) <=> (~b(elem!1, s(s(elem!1))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3762])).
% 0.86/1.12 tff(3764,plain,
% 0.86/1.12 (b(s(s(s(z))), z) <=> b(s(s(elem!1)), z)),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3756])).
% 0.86/1.12 tff(3765,plain,
% 0.86/1.12 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 0.86/1.12 inference(symmetry,[status(thm)],[3764])).
% 0.86/1.12 tff(3766,plain,
% 0.86/1.12 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1176, 3735, 2790])).
% 0.86/1.12 tff(3767,plain,
% 0.86/1.12 (b(s(s(s(elem!1))), s(elem!1))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[293, 3766, 11])).
% 0.86/1.12 tff(3768,plain,
% 0.86/1.12 (~r(s(s(elem!1)), z)),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3157, 3767, 2790, 57, 3735])).
% 0.86/1.12 tff(3769,plain,
% 0.86/1.12 (b(s(s(elem!1)), z)),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[228, 3768])).
% 0.86/1.12 tff(3770,plain,
% 0.86/1.12 (b(s(s(s(z))), z)),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3769, 3765])).
% 0.86/1.12 tff(3771,plain,
% 0.86/1.12 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3598, 3597])).
% 0.86/1.12 tff(3772,plain,
% 0.86/1.12 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3596])).
% 0.86/1.12 tff(3773,plain,
% 0.86/1.12 (r(s(elem!1), s(z))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[168, 3772])).
% 0.86/1.12 tff(3774,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 0.86/1.12 tff(3775,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(3776,plain,
% 0.86/1.12 (((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(3777,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3776])).
% 0.86/1.12 tff(3778,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[3777, 3775])).
% 0.86/1.12 tff(3779,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), z)))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(3780,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(z, s(z)))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3779, 3778])).
% 0.86/1.12 tff(3781,plain,
% 0.86/1.12 ($false),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3780, 180, 270, 485, 3774])).
% 0.86/1.12 tff(3782,plain,((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.86/1.12 tff(3783,plain,
% 0.86/1.12 (~r(z, s(z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3782, 3773, 2790])).
% 0.86/1.12 tff(3784,plain,
% 0.86/1.12 (b(z, s(z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[505, 3783])).
% 0.86/1.12 tff(3785,plain,
% 0.86/1.12 (~b(s(s(elem!1)), s(z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[2363, 3769, 3784])).
% 0.86/1.12 tff(3786,plain,
% 0.86/1.12 (r(s(s(elem!1)), s(z))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[778, 3785])).
% 0.86/1.12 tff(3787,plain,
% 0.86/1.12 ((elem!1 = s(elem!1)) <=> (s(z) = s(elem!1))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3596])).
% 0.86/1.12 tff(3788,plain,
% 0.86/1.12 ((elem!1 = s(elem!1)) <=> (s(elem!1) = s(z))),
% 0.86/1.12 inference(transitivity,[status(thm)],[3787, 84])).
% 0.86/1.12 tff(3789,plain,
% 0.86/1.12 ((elem!1 = s(elem!1)) <=> (s(z) = s(elem!1))),
% 0.86/1.12 inference(transitivity,[status(thm)],[3788, 85])).
% 0.86/1.12 tff(3790,plain,
% 0.86/1.12 ((~(elem!1 = s(elem!1))) <=> (~(s(z) = s(elem!1)))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3789])).
% 0.86/1.12 tff(3791,plain,
% 0.86/1.12 (~(s(z) = s(elem!1))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[46, 3790])).
% 0.86/1.12 tff(3792,plain,
% 0.86/1.12 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3596])).
% 0.86/1.12 tff(3793,plain,
% 0.86/1.12 (b(s(s(s(elem!1))), s(z))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3733, 3792])).
% 0.86/1.12 tff(3794,plain,
% 0.86/1.12 (~b(s(z), s(elem!1))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[907, 3793, 3767])).
% 0.86/1.12 tff(3795,plain,
% 0.86/1.12 (r(s(z), s(elem!1))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[467, 3794, 3791])).
% 0.86/1.12 tff(3796,plain,
% 0.86/1.12 (~r(s(s(elem!1)), s(elem!1))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[858, 3795, 3786])).
% 0.86/1.12 tff(3797,plain,
% 0.86/1.12 (b(s(s(elem!1)), s(elem!1))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[605, 3796, 57])).
% 0.86/1.12 tff(3798,plain,
% 0.86/1.12 (b(s(s(s(z))), s(s(z)))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3797, 3771])).
% 0.86/1.12 tff(3799,plain,
% 0.86/1.12 (r(elem!1, z) <=> r(s(z), z)),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3596])).
% 0.86/1.12 tff(3800,plain,
% 0.86/1.12 ((~r(elem!1, z)) <=> (~r(s(z), z))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3799])).
% 0.86/1.12 tff(3801,plain,
% 0.86/1.12 (~r(s(z), z)),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[2791, 3800])).
% 0.86/1.12 tff(3802,plain,
% 0.86/1.12 (b(s(z), z)),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[794, 3801])).
% 0.86/1.12 tff(3803,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(3804,plain,
% 0.86/1.12 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(3805,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3804])).
% 0.86/1.12 tff(3806,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 0.86/1.12 inference(transitivity,[status(thm)],[3805, 3803])).
% 0.86/1.12 tff(3807,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(z), s(s(s(z))))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(3808,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3807, 3806])).
% 0.86/1.12 tff(3809,plain,
% 0.86/1.12 (~b(s(z), s(s(s(z))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3808, 206, 3802, 3798, 3770])).
% 0.86/1.12 tff(3810,plain,
% 0.86/1.12 (~b(elem!1, s(s(elem!1)))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3809, 3763])).
% 0.86/1.12 tff(3811,plain,
% 0.86/1.12 (r(elem!1, s(s(elem!1)))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[889, 3810, 24])).
% 0.86/1.12 tff(3812,plain,
% 0.86/1.12 (r(s(z), s(s(s(z))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3811, 3758])).
% 0.86/1.12 tff(3813,plain,
% 0.86/1.12 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(s(z)))), s(s(z)))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3599, 3597])).
% 0.86/1.12 tff(3814,plain,
% 0.86/1.12 (b(s(s(s(s(z)))), s(s(z)))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3767, 3813])).
% 0.86/1.12 tff(3815,plain,
% 0.86/1.12 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1269, 206, 3798, 3814])).
% 0.86/1.12 tff(3816,plain,
% 0.86/1.12 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1295, 3596])).
% 0.86/1.12 tff(3817,plain,
% 0.86/1.12 (r(s(s(s(s(z)))), s(s(s(z))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[1299, 150, 3816, 3815])).
% 0.86/1.12 tff(3818,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(3819,plain,
% 0.86/1.12 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.86/1.12 inference(rewrite,[status(thm)],[])).
% 0.86/1.12 tff(3820,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))))),
% 0.86/1.12 inference(monotonicity,[status(thm)],[3819])).
% 0.86/1.12 tff(3821,plain,
% 0.86/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.86/1.12 inference(transitivity,[status(thm)],[3820, 3818])).
% 0.86/1.12 tff(3822,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.86/1.12 inference(quant_inst,[status(thm)],[])).
% 0.86/1.12 tff(3823,plain,
% 0.86/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(s(z))))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3822, 3821])).
% 0.86/1.12 tff(3824,plain,
% 0.86/1.12 (~r(s(z), s(s(s(s(z)))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[3823, 180, 3817, 3812])).
% 0.86/1.12 tff(3825,plain,
% 0.86/1.12 (~r(elem!1, s(s(s(elem!1))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3824, 3755])).
% 0.86/1.12 tff(3826,plain,
% 0.86/1.12 (b(elem!1, s(s(s(elem!1))))),
% 0.86/1.12 inference(unit_resolution,[status(thm)],[533, 3825, 419])).
% 0.86/1.12 tff(3827,plain,
% 0.86/1.12 (b(s(z), s(s(s(s(z)))))),
% 0.86/1.12 inference(modus_ponens,[status(thm)],[3826, 3750])).
% 0.97/1.12 tff(3828,plain,
% 0.97/1.12 (r(s(s(z)), s(z))),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[1460, 3596, 168])).
% 0.97/1.12 tff(3829,plain,
% 0.97/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.97/1.12 inference(rewrite,[status(thm)],[])).
% 0.97/1.12 tff(3830,plain,
% 0.97/1.12 (((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.97/1.12 inference(rewrite,[status(thm)],[])).
% 0.97/1.12 tff(3831,plain,
% 0.97/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 0.97/1.12 inference(monotonicity,[status(thm)],[3830])).
% 0.97/1.12 tff(3832,plain,
% 0.97/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.97/1.12 inference(transitivity,[status(thm)],[3831, 3829])).
% 0.97/1.12 tff(3833,plain,
% 0.97/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.97/1.12 inference(quant_inst,[status(thm)],[])).
% 0.97/1.12 tff(3834,plain,
% 0.97/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.97/1.12 inference(modus_ponens,[status(thm)],[3833, 3832])).
% 0.97/1.12 tff(3835,plain,
% 0.97/1.12 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[3834, 206, 2074, 2564])).
% 0.97/1.12 tff(3836,plain,
% 0.97/1.12 (r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[2688, 150, 2649, 3835])).
% 0.97/1.12 tff(3837,plain,
% 0.97/1.12 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[2571, 206, 796, 2564, 2565])).
% 0.97/1.12 tff(3838,plain,
% 0.97/1.12 (r(s(s(s(s(s(elem!1))))), s(z))),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[2578, 3837])).
% 0.97/1.12 tff(3839,plain,
% 0.97/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z))))),
% 0.97/1.12 inference(rewrite,[status(thm)],[])).
% 0.97/1.12 tff(3840,plain,
% 0.97/1.12 (((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z))))),
% 0.97/1.12 inference(rewrite,[status(thm)],[])).
% 0.97/1.12 tff(3841,plain,
% 0.97/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z)))))),
% 0.97/1.12 inference(monotonicity,[status(thm)],[3840])).
% 0.97/1.12 tff(3842,plain,
% 0.97/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z))))),
% 0.97/1.12 inference(transitivity,[status(thm)],[3841, 3839])).
% 0.97/1.12 tff(3843,plain,
% 0.97/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))))),
% 0.97/1.12 inference(quant_inst,[status(thm)],[])).
% 0.97/1.12 tff(3844,plain,
% 0.97/1.12 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(z)))),
% 0.97/1.12 inference(modus_ponens,[status(thm)],[3843, 3842])).
% 0.97/1.12 tff(3845,plain,
% 0.97/1.12 ($false),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[3844, 180, 3838, 1422, 3836])).
% 0.97/1.12 tff(3846,plain,((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z))))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.12 tff(3847,plain,
% 0.97/1.12 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[3846, 3828, 3802, 3827, 3749])).
% 0.97/1.12 tff(3848,plain,
% 0.97/1.12 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.97/1.12 inference(modus_ponens,[status(thm)],[3847, 3606])).
% 0.97/1.12 tff(3849,plain,
% 0.97/1.12 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[2431, 3848, 3603])).
% 0.97/1.12 tff(3850,plain,
% 0.97/1.12 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.97/1.12 inference(modus_ponens,[status(thm)],[3849, 3602])).
% 0.97/1.12 tff(3851,plain,
% 0.97/1.12 (r(z, s(s(s(s(z))))) <=> r(z, s(s(s(elem!1))))),
% 0.97/1.12 inference(monotonicity,[status(thm)],[3600])).
% 0.97/1.12 tff(3852,plain,
% 0.97/1.12 (r(z, s(s(s(elem!1)))) <=> r(z, s(s(s(s(z)))))),
% 0.97/1.12 inference(symmetry,[status(thm)],[3851])).
% 0.97/1.12 tff(3853,plain,
% 0.97/1.12 (b(z, s(s(s(s(z))))) <=> b(z, s(s(s(elem!1))))),
% 0.97/1.12 inference(monotonicity,[status(thm)],[3600])).
% 0.97/1.12 tff(3854,plain,
% 0.97/1.12 ((~b(z, s(s(s(s(z)))))) <=> (~b(z, s(s(s(elem!1)))))),
% 0.97/1.12 inference(monotonicity,[status(thm)],[3853])).
% 0.97/1.12 tff(3855,plain,
% 0.97/1.12 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 0.97/1.12 inference(monotonicity,[status(thm)],[3620])).
% 0.97/1.12 tff(3856,plain,
% 0.97/1.12 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 0.97/1.12 inference(symmetry,[status(thm)],[3855])).
% 0.97/1.12 tff(3857,plain,
% 0.97/1.12 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 0.97/1.12 inference(monotonicity,[status(thm)],[3600, 3596])).
% 0.97/1.12 tff(3858,plain,
% 0.97/1.12 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 0.97/1.12 inference(symmetry,[status(thm)],[3857])).
% 0.97/1.12 tff(3859,plain,
% 0.97/1.12 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(z)))), elem!1)),
% 0.97/1.12 inference(transitivity,[status(thm)],[3792, 3858])).
% 0.97/1.12 tff(3860,plain,
% 0.97/1.12 (b(s(s(s(s(z)))), elem!1)),
% 0.97/1.12 inference(modus_ponens,[status(thm)],[3733, 3859])).
% 0.97/1.12 tff(3861,plain,
% 0.97/1.12 (b(s(s(s(s(z)))), s(z))),
% 0.97/1.12 inference(modus_ponens,[status(thm)],[3860, 3856])).
% 0.97/1.12 tff(3862,plain,
% 0.97/1.12 ((~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[2664, 206, 3784])).
% 0.97/1.12 tff(3863,plain,
% 0.97/1.12 (~b(z, s(s(s(s(z)))))),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[3862, 3861])).
% 0.97/1.12 tff(3864,plain,
% 0.97/1.12 (~b(z, s(s(s(elem!1))))),
% 0.97/1.12 inference(modus_ponens,[status(thm)],[3863, 3854])).
% 0.97/1.12 tff(3865,plain,
% 0.97/1.12 (r(z, s(s(s(elem!1))))),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[1985, 3864])).
% 0.97/1.12 tff(3866,plain,
% 0.97/1.12 (r(z, s(s(s(s(z)))))),
% 0.97/1.12 inference(modus_ponens,[status(thm)],[3865, 3852])).
% 0.97/1.12 tff(3867,plain,
% 0.97/1.12 (~r(s(s(s(s(s(elem!1))))), z)),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[2674, 180, 3866, 3850])).
% 0.97/1.12 tff(3868,plain,
% 0.97/1.12 (b(s(s(s(s(s(elem!1))))), z)),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[2388, 150, 1395, 3867])).
% 0.97/1.12 tff(3869,plain,
% 0.97/1.12 (~(s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 0.97/1.12 inference(unit_resolution,[status(thm)],[2439, 3596])).
% 0.97/1.12 tff(3870,plain,
% 0.97/1.12 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.97/1.12 inference(rewrite,[status(thm)],[])).
% 0.97/1.12 tff(3871,plain,
% 0.97/1.12 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3872,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 0.97/1.13 inference(monotonicity,[status(thm)],[3871])).
% 0.97/1.13 tff(3873,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.97/1.13 inference(transitivity,[status(thm)],[3872, 3870])).
% 0.97/1.13 tff(3874,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.97/1.13 inference(quant_inst,[status(thm)],[])).
% 0.97/1.13 tff(3875,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 0.97/1.13 inference(modus_ponens,[status(thm)],[3874, 3873])).
% 0.97/1.13 tff(3876,plain,
% 0.97/1.13 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3875, 206, 3798, 3814, 3861])).
% 0.97/1.13 tff(3877,plain,
% 0.97/1.13 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[2467, 3816])).
% 0.97/1.13 tff(3878,plain,
% 0.97/1.13 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[2471, 150, 3877, 3876])).
% 0.97/1.13 tff(3879,plain,
% 0.97/1.13 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[2487, 3849, 3878, 3596])).
% 0.97/1.13 tff(3880,plain,
% 0.97/1.13 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[2455, 150, 3879, 3869])).
% 0.97/1.13 tff(3881,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3882,plain,
% 0.97/1.13 (((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3883,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z))))),
% 0.97/1.13 inference(monotonicity,[status(thm)],[3882])).
% 0.97/1.13 tff(3884,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z)))),
% 0.97/1.13 inference(transitivity,[status(thm)],[3883, 3881])).
% 0.97/1.13 tff(3885,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 0.97/1.13 inference(quant_inst,[status(thm)],[])).
% 0.97/1.13 tff(3886,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), z))),
% 0.97/1.13 inference(modus_ponens,[status(thm)],[3885, 3884])).
% 0.97/1.13 tff(3887,plain,
% 0.97/1.13 ($false),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3886, 206, 3880, 3770, 3868])).
% 0.97/1.13 tff(3888,plain,(r(elem!1, s(z)) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.97/1.13 tff(3889,plain,
% 0.97/1.13 (r(elem!1, s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3888, 62, 58, 11])).
% 0.97/1.13 tff(3890,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3891,plain,
% 0.97/1.13 (((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3892,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))))),
% 0.97/1.13 inference(monotonicity,[status(thm)],[3891])).
% 0.97/1.13 tff(3893,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))))),
% 0.97/1.13 inference(transitivity,[status(thm)],[3892, 3890])).
% 0.97/1.13 tff(3894,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z))) | (~r(s(elem!1), elem!1)))),
% 0.97/1.13 inference(quant_inst,[status(thm)],[])).
% 0.97/1.13 tff(3895,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(elem!1, s(z)))),
% 0.97/1.13 inference(modus_ponens,[status(thm)],[3894, 3893])).
% 0.97/1.13 tff(3896,plain,
% 0.97/1.13 ($false),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3895, 180, 170, 441, 3774])).
% 0.97/1.13 tff(3897,plain,((~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.13 tff(3898,plain,
% 0.97/1.13 (~r(s(elem!1), s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3897, 168, 3889])).
% 0.97/1.13 tff(3899,plain,
% 0.97/1.13 (b(s(elem!1), s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[1652, 99, 3898])).
% 0.97/1.13 tff(3900,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 0.97/1.13 tff(3901,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3902,plain,
% 0.97/1.13 (((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3903,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))))),
% 0.97/1.13 inference(monotonicity,[status(thm)],[3902])).
% 0.97/1.13 tff(3904,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z))))),
% 0.97/1.13 inference(transitivity,[status(thm)],[3903, 3901])).
% 0.97/1.13 tff(3905,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(elem!1), s(z))) | (~b(z, s(z))) | (~b(s(elem!1), z)))),
% 0.97/1.13 inference(quant_inst,[status(thm)],[])).
% 0.97/1.13 tff(3906,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~b(s(elem!1), s(z)))),
% 0.97/1.13 inference(modus_ponens,[status(thm)],[3905, 3904])).
% 0.97/1.13 tff(3907,plain,
% 0.97/1.13 (~b(s(elem!1), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3906, 206, 911, 3900])).
% 0.97/1.13 tff(3908,plain,
% 0.97/1.13 (~b(s(s(elem!1)), elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3706, 797, 196])).
% 0.97/1.13 tff(3909,plain,
% 0.97/1.13 ((s(s(elem!1)) = elem!1) | r(s(s(elem!1)), elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[267, 150, 3908])).
% 0.97/1.13 tff(3910,plain,
% 0.97/1.13 (r(s(s(elem!1)), elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3909, 3191])).
% 0.97/1.13 tff(3911,plain,
% 0.97/1.13 (~r(s(s(elem!1)), s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3694, 3910, 441])).
% 0.97/1.13 tff(3912,plain,
% 0.97/1.13 (b(s(s(elem!1)), s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[776, 150, 3911, 772])).
% 0.97/1.13 tff(3913,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3914,plain,
% 0.97/1.13 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3915,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, elem!1))))),
% 0.97/1.13 inference(monotonicity,[status(thm)],[3914])).
% 0.97/1.13 tff(3916,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 0.97/1.13 inference(transitivity,[status(thm)],[3915, 3913])).
% 0.97/1.13 tff(3917,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 0.97/1.13 inference(quant_inst,[status(thm)],[])).
% 0.97/1.13 tff(3918,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(z, elem!1))),
% 0.97/1.13 inference(modus_ponens,[status(thm)],[3917, 3916])).
% 0.97/1.13 tff(3919,plain,
% 0.97/1.13 ($false),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3918, 206, 797, 196, 911, 3912])).
% 0.97/1.13 tff(3920,plain,((~b(z, elem!1)) | (~b(s(s(elem!1)), z)) | (~b(z, s(z))) | (~r(elem!1, s(z))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.13 tff(3921,plain,
% 0.97/1.13 (~b(z, elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3920, 911, 441, 196, 27])).
% 0.97/1.13 tff(3922,plain,
% 0.97/1.13 (r(z, elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[556, 3921, 109])).
% 0.97/1.13 tff(3923,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3924,plain,
% 0.97/1.13 (((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3925,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1))))),
% 0.97/1.13 inference(monotonicity,[status(thm)],[3924])).
% 0.97/1.13 tff(3926,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1)))),
% 0.97/1.13 inference(transitivity,[status(thm)],[3925, 3923])).
% 0.97/1.13 tff(3927,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1)) | (~r(s(elem!1), z)))),
% 0.97/1.13 inference(quant_inst,[status(thm)],[])).
% 0.97/1.13 tff(3928,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (~r(z, elem!1))),
% 0.97/1.13 inference(modus_ponens,[status(thm)],[3927, 3926])).
% 0.97/1.13 tff(3929,plain,
% 0.97/1.13 (~r(s(elem!1), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3928, 180, 170, 3922])).
% 0.97/1.13 tff(3930,plain,
% 0.97/1.13 ($false),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[283, 3929, 3907])).
% 0.97/1.13 tff(3931,plain,((~b(z, s(z))) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))) | (z = elem!1) | (~r(elem!1, s(z))) | (~b(s(s(elem!1)), z)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.13 tff(3932,plain,
% 0.97/1.13 (~b(z, s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3931, 196, 3899, 240, 3889, 168, 24])).
% 0.97/1.13 tff(3933,plain,
% 0.97/1.13 (r(z, s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[505, 3932])).
% 0.97/1.13 tff(3934,plain,
% 0.97/1.13 (~r(z, elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3670, 180, 3889, 3933])).
% 0.97/1.13 tff(3935,plain,
% 0.97/1.13 (b(z, elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[556, 3934, 240])).
% 0.97/1.13 tff(3936,plain,
% 0.97/1.13 (~b(s(s(elem!1)), elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3706, 3935, 196])).
% 0.97/1.13 tff(3937,plain,
% 0.97/1.13 (r(s(s(elem!1)), elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[267, 150, 3936, 30])).
% 0.97/1.13 tff(3938,plain,
% 0.97/1.13 (~r(s(s(s(elem!1))), elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3699, 3937, 83, 3889])).
% 0.97/1.13 tff(3939,plain,
% 0.97/1.13 (b(s(s(s(elem!1))), elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[320, 3938, 58])).
% 0.97/1.13 tff(3940,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3941,plain,
% 0.97/1.13 (((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3942,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z)))))),
% 0.97/1.13 inference(monotonicity,[status(thm)],[3941])).
% 0.97/1.13 tff(3943,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 0.97/1.13 inference(transitivity,[status(thm)],[3942, 3940])).
% 0.97/1.13 tff(3944,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, z)))),
% 0.97/1.13 inference(quant_inst,[status(thm)],[])).
% 0.97/1.13 tff(3945,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 0.97/1.13 inference(modus_ponens,[status(thm)],[3944, 3943])).
% 0.97/1.13 tff(3946,plain,
% 0.97/1.13 (~r(elem!1, z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3945, 180, 3889, 3933])).
% 0.97/1.13 tff(3947,plain,
% 0.97/1.13 (~r(s(s(elem!1)), s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3694, 3937, 3889])).
% 0.97/1.13 tff(3948,plain,
% 0.97/1.13 (b(s(s(elem!1)), s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[778, 3947])).
% 0.97/1.13 tff(3949,plain,
% 0.97/1.13 (~r(s(s(elem!1)), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[263, 3937, 168])).
% 0.97/1.13 tff(3950,plain,
% 0.97/1.13 (b(s(s(elem!1)), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[605, 3949, 57])).
% 0.97/1.13 tff(3951,plain,
% 0.97/1.13 (~b(s(z), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[615, 3950, 3948])).
% 0.97/1.13 tff(3952,plain,
% 0.97/1.13 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3240, 3951, 3889, 46, 3946, 99, 3939])).
% 0.97/1.13 tff(3953,plain,
% 0.97/1.13 (~b(elem!1, z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[662, 357, 654])).
% 0.97/1.13 tff(3954,plain,
% 0.97/1.13 (r(elem!1, z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[387, 3953, 135])).
% 0.97/1.13 tff(3955,plain,
% 0.97/1.13 (~r(s(elem!1), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[650, 3954, 168])).
% 0.97/1.13 tff(3956,plain,
% 0.97/1.13 (b(s(elem!1), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[283, 3955])).
% 0.97/1.13 tff(3957,plain,
% 0.97/1.13 (~b(s(s(elem!1)), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[214, 3956, 196])).
% 0.97/1.13 tff(3958,plain,
% 0.97/1.13 (r(s(s(elem!1)), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[605, 3957, 57])).
% 0.97/1.13 tff(3959,plain,
% 0.97/1.13 (b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[333, 3958, 58, 62, 11])).
% 0.97/1.13 tff(3960,plain,
% 0.97/1.13 ($false),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[723, 206, 357, 3956, 3959])).
% 0.97/1.13 tff(3961,plain,((~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = elem!1) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(s(elem!1)), z)) | (elem!1 = z) | (~b(s(s(s(elem!1))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.13 tff(3962,plain,
% 0.97/1.13 (~b(s(s(s(elem!1))), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3961, 3939, 62, 11, 196, 620, 58])).
% 0.97/1.13 tff(3963,plain,
% 0.97/1.13 (r(s(s(s(elem!1))), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[372, 3962])).
% 0.97/1.13 tff(3964,plain,
% 0.97/1.13 (~b(s(elem!1), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[214, 3950, 196])).
% 0.97/1.13 tff(3965,plain,
% 0.97/1.13 (r(s(elem!1), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[283, 3964])).
% 0.97/1.13 tff(3966,plain,
% 0.97/1.13 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[1176, 3965, 3963])).
% 0.97/1.13 tff(3967,plain,
% 0.97/1.13 ($false),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[293, 3966, 3952, 11])).
% 0.97/1.13 tff(3968,plain,((~b(s(s(elem!1)), z)) | (s(s(s(elem!1))) = s(elem!1)) | (s(elem!1) = s(z)) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.97/1.13 tff(3969,plain,
% 0.97/1.13 (~b(s(s(elem!1)), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3968, 90, 11, 62, 58])).
% 0.97/1.13 tff(3970,plain,
% 0.97/1.13 (r(s(s(elem!1)), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[228, 3969])).
% 0.97/1.13 tff(3971,plain,
% 0.97/1.13 (~r(elem!1, z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[650, 270, 168])).
% 0.97/1.13 tff(3972,plain,
% 0.97/1.13 (b(elem!1, z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[387, 3971, 2794])).
% 0.97/1.13 tff(3973,plain,
% 0.97/1.13 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3157, 270, 241, 57, 60])).
% 0.97/1.13 tff(3974,plain,
% 0.97/1.13 (~r(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[1176, 270, 60])).
% 0.97/1.13 tff(3975,plain,
% 0.97/1.13 ($false),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[293, 3974, 3973, 11])).
% 0.97/1.13 tff(3976,plain,((~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.13 tff(3977,plain,
% 0.97/1.13 (~r(s(s(s(elem!1))), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3976, 270, 11, 3970])).
% 0.97/1.13 tff(3978,plain,
% 0.97/1.13 (b(s(s(s(elem!1))), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[372, 3977])).
% 0.97/1.13 tff(3979,plain,
% 0.97/1.13 (~b(s(s(s(elem!1))), elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[662, 3978, 3972])).
% 0.97/1.13 tff(3980,plain,
% 0.97/1.13 (r(s(s(s(elem!1))), elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[320, 3979, 58])).
% 0.97/1.13 tff(3981,plain,
% 0.97/1.13 (b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[315, 3980, 62, 11])).
% 0.97/1.13 tff(3982,plain,
% 0.97/1.13 (b(elem!1, s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3732, 3979, 58, 2794, 11])).
% 0.97/1.13 tff(3983,plain,
% 0.97/1.13 (b(s(s(s(elem!1))), s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3103, 3982, 62, 11, 58, 65, 3971])).
% 0.97/1.13 tff(3984,plain,
% 0.97/1.13 (~b(s(z), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[907, 3983, 3981])).
% 0.97/1.13 tff(3985,plain,
% 0.97/1.13 (r(s(z), s(elem!1))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[467, 3984, 59])).
% 0.97/1.13 tff(3986,plain,
% 0.97/1.13 (~b(s(z), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[828, 3983, 3978])).
% 0.97/1.13 tff(3987,plain,
% 0.97/1.13 (r(s(z), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[794, 3986])).
% 0.97/1.13 tff(3988,plain,
% 0.97/1.13 ($false),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3718, 180, 270, 3987, 3985])).
% 0.97/1.13 tff(3989,plain,((~r(s(elem!1), z)) | (s(z) = s(elem!1)) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.13 tff(3990,plain,
% 0.97/1.13 (~r(s(elem!1), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3989, 59, 62, 11, 58, 65])).
% 0.97/1.13 tff(3991,plain,
% 0.97/1.13 (b(s(elem!1), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[283, 3990])).
% 0.97/1.13 tff(3992,plain,
% 0.97/1.13 (~r(s(s(s(elem!1))), elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[3674, 3991, 11, 3889, 2794, 58])).
% 0.97/1.13 tff(3993,plain,
% 0.97/1.13 (b(s(s(s(elem!1))), elem!1)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[320, 3992, 58])).
% 0.97/1.13 tff(3994,plain,
% 0.97/1.13 (b(s(elem!1), s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[1652, 90, 3898])).
% 0.97/1.13 tff(3995,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3996,plain,
% 0.97/1.13 (((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(3997,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))))),
% 0.97/1.13 inference(monotonicity,[status(thm)],[3996])).
% 0.97/1.13 tff(3998,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 0.97/1.13 inference(transitivity,[status(thm)],[3997, 3995])).
% 0.97/1.13 tff(3999,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 0.97/1.13 inference(quant_inst,[status(thm)],[])).
% 0.97/1.13 tff(4000,plain,
% 0.97/1.13 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))),
% 0.97/1.13 inference(modus_ponens,[status(thm)],[3999, 3998])).
% 0.97/1.13 tff(4001,plain,
% 0.97/1.13 ($false),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[4000, 206, 95, 796, 3900])).
% 0.97/1.13 tff(4002,plain,((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.13 tff(4003,plain,
% 0.97/1.13 (~b(s(z), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[4002, 3991, 3994])).
% 0.97/1.13 tff(4004,plain,
% 0.97/1.13 (r(s(z), z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[794, 4003])).
% 0.97/1.13 tff(4005,plain,
% 0.97/1.13 (~r(s(s(elem!1)), s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[789, 4004, 3970])).
% 0.97/1.13 tff(4006,plain,
% 0.97/1.13 (b(s(s(elem!1)), s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[778, 4005])).
% 0.97/1.13 tff(4007,plain,
% 0.97/1.13 (~r(s(s(s(elem!1))), s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[725, 4006, 58, 65, 90, 11, 62, 3970])).
% 0.97/1.13 tff(4008,plain,
% 0.97/1.13 (b(s(s(s(elem!1))), s(z))),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[733, 4007])).
% 0.97/1.13 tff(4009,plain,
% 0.97/1.13 (~b(elem!1, z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[662, 654, 357])).
% 0.97/1.13 tff(4010,plain,
% 0.97/1.13 (r(elem!1, z)),
% 0.97/1.13 inference(unit_resolution,[status(thm)],[387, 4009, 135])).
% 0.97/1.13 tff(4011,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(4012,plain,
% 0.97/1.13 (((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))) <=> ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 0.97/1.13 inference(rewrite,[status(thm)],[])).
% 0.97/1.13 tff(4013,plain,
% 0.97/1.13 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4012])).
% 0.97/1.14 tff(4014,plain,
% 0.97/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 0.97/1.14 inference(transitivity,[status(thm)],[4013, 4011])).
% 0.97/1.14 tff(4015,plain,
% 0.97/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z))))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(4016,plain,
% 0.97/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), z)) | (~r(elem!1, s(z)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[4015, 4014])).
% 0.97/1.14 tff(4017,plain,
% 0.97/1.14 (~r(elem!1, s(z))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[4016, 180, 4010, 3111])).
% 0.97/1.14 tff(4018,plain,
% 0.97/1.14 (b(elem!1, s(z))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[154, 4017, 65])).
% 0.97/1.14 tff(4019,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[741, 206, 654, 4018, 735])).
% 0.97/1.14 tff(4020,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (elem!1 = s(z)) | (elem!1 = z) | (~b(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(4021,plain,
% 0.97/1.14 (~b(s(s(s(elem!1))), z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[4020, 4008, 65, 2794, 3993])).
% 0.97/1.14 tff(4022,plain,
% 0.97/1.14 (r(s(s(s(elem!1))), z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[372, 4021])).
% 0.97/1.14 tff(4023,plain,
% 0.97/1.14 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[588, 4022, 3970])).
% 0.97/1.14 tff(4024,plain,
% 0.97/1.14 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[759, 4008, 4006])).
% 0.97/1.14 tff(4025,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[577, 150, 4024, 4023, 83])).
% 0.97/1.14 tff(4026,plain,((s(z) = s(elem!1)) | (elem!1 = s(z)) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(4027,plain,
% 0.97/1.14 (s(z) = s(elem!1)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[4026, 65, 58, 11, 62])).
% 0.97/1.14 tff(4028,plain,
% 0.97/1.14 (s(elem!1) = s(z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[101, 4027])).
% 0.97/1.14 tff(4029,plain,
% 0.97/1.14 (z = elem!1),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[111, 4028])).
% 0.97/1.14 tff(4030,plain,
% 0.97/1.14 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4029])).
% 0.97/1.14 tff(4031,plain,
% 0.97/1.14 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(transitivity,[status(thm)],[4030, 63])).
% 0.97/1.14 tff(4032,plain,
% 0.97/1.14 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.97/1.14 inference(transitivity,[status(thm)],[4031, 64])).
% 0.97/1.14 tff(4033,plain,
% 0.97/1.14 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4032])).
% 0.97/1.14 tff(4034,plain,
% 0.97/1.14 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[1395, 4033])).
% 0.97/1.14 tff(4035,plain,
% 0.97/1.14 (s(s(z)) = s(s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4027])).
% 0.97/1.14 tff(4036,plain,
% 0.97/1.14 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4035])).
% 0.97/1.14 tff(4037,plain,
% 0.97/1.14 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4036, 4027])).
% 0.97/1.14 tff(4038,plain,
% 0.97/1.14 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4037])).
% 0.97/1.14 tff(4039,plain,
% 0.97/1.14 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4027])).
% 0.97/1.14 tff(4040,plain,
% 0.97/1.14 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(z))), s(z))),
% 0.97/1.14 inference(transitivity,[status(thm)],[4039, 4038])).
% 0.97/1.14 tff(4041,plain,
% 0.97/1.14 (~b(s(elem!1), z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[139, 4027, 62])).
% 0.97/1.14 tff(4042,plain,
% 0.97/1.14 (r(s(elem!1), z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[283, 4041])).
% 0.97/1.14 tff(4043,plain,
% 0.97/1.14 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4027])).
% 0.97/1.14 tff(4044,plain,
% 0.97/1.14 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
% 0.97/1.14 inference(symmetry,[status(thm)],[4043])).
% 0.97/1.14 tff(4045,plain,
% 0.97/1.14 (r(s(z), elem!1)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[168, 4044])).
% 0.97/1.14 tff(4046,plain,
% 0.97/1.14 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[112])).
% 0.97/1.14 tff(4047,plain,
% 0.97/1.14 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(transitivity,[status(thm)],[4046, 63])).
% 0.97/1.14 tff(4048,plain,
% 0.97/1.14 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.97/1.14 inference(transitivity,[status(thm)],[4047, 64])).
% 0.97/1.14 tff(4049,plain,
% 0.97/1.14 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4048])).
% 0.97/1.14 tff(4050,plain,
% 0.97/1.14 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[1395, 4049])).
% 0.97/1.14 tff(4051,plain,
% 0.97/1.14 (s(s(z)) = s(s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[97])).
% 0.97/1.14 tff(4052,plain,
% 0.97/1.14 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4051])).
% 0.97/1.14 tff(4053,plain,
% 0.97/1.14 (b(s(s(s(z))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4052, 97])).
% 0.97/1.14 tff(4054,plain,
% 0.97/1.14 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(z))), s(z))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4053])).
% 0.97/1.14 tff(4055,plain,
% 0.97/1.14 (~r(s(s(s(elem!1))), z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[3976, 241, 11, 270])).
% 0.97/1.14 tff(4056,plain,
% 0.97/1.14 (b(s(s(s(elem!1))), z)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[372, 4055])).
% 0.97/1.14 tff(4057,plain,
% 0.97/1.14 (r(z, s(z)) <=> r(z, s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[97])).
% 0.97/1.14 tff(4058,plain,
% 0.97/1.14 (r(z, s(elem!1)) <=> r(z, s(z))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4057])).
% 0.97/1.14 tff(4059,plain,
% 0.97/1.14 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[112])).
% 0.97/1.14 tff(4060,plain,
% 0.97/1.14 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4059])).
% 0.97/1.14 tff(4061,plain,
% 0.97/1.14 (r(elem!1, s(elem!1)) <=> r(z, s(z))),
% 0.97/1.14 inference(transitivity,[status(thm)],[4060, 4058])).
% 0.97/1.14 tff(4062,plain,
% 0.97/1.14 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[97])).
% 0.97/1.14 tff(4063,plain,
% 0.97/1.14 (r(elem!1, s(elem!1))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[441, 4062])).
% 0.97/1.14 tff(4064,plain,
% 0.97/1.14 (r(z, s(z))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[4063, 4061])).
% 0.97/1.14 tff(4065,plain,
% 0.97/1.14 (r(s(s(z)), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4051])).
% 0.97/1.14 tff(4066,plain,
% 0.97/1.14 (r(s(s(elem!1)), elem!1) <=> r(s(s(z)), elem!1)),
% 0.97/1.14 inference(symmetry,[status(thm)],[4065])).
% 0.97/1.14 tff(4067,plain,
% 0.97/1.14 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[112])).
% 0.97/1.14 tff(4068,plain,
% 0.97/1.14 (r(s(s(elem!1)), z) <=> r(s(s(z)), elem!1)),
% 0.97/1.14 inference(transitivity,[status(thm)],[4067, 4066])).
% 0.97/1.14 tff(4069,plain,
% 0.97/1.14 (r(s(s(z)), elem!1)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[241, 4068])).
% 0.97/1.14 tff(4070,plain,
% 0.97/1.14 (b(s(s(elem!1)), s(elem!1))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[605, 3152, 57])).
% 0.97/1.14 tff(4071,plain,
% 0.97/1.14 (s(s(elem!1)) = s(s(z))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4051])).
% 0.97/1.14 tff(4072,plain,
% 0.97/1.14 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) <=> (s(s(z)) = s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4071])).
% 0.97/1.14 tff(4073,plain,
% 0.97/1.14 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(z)))),
% 0.97/1.14 inference(transitivity,[status(thm)],[4072, 2642])).
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% 0.97/1.14 ((s(s(s(s(s(elem!1))))) = s(s(z))) <=> (s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4073])).
% 0.97/1.14 tff(4075,plain,
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% 0.97/1.14 inference(monotonicity,[status(thm)],[4074])).
% 0.97/1.14 tff(4076,plain,
% 0.97/1.14 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[2650, 4075])).
% 0.97/1.14 tff(4077,plain,
% 0.97/1.14 (r(s(s(elem!1)), s(s(s(s(s(elem!1)))))) <=> r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4071])).
% 0.97/1.14 tff(4078,plain,
% 0.97/1.14 (r(s(s(z)), s(s(s(s(s(elem!1)))))) <=> r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4077])).
% 0.97/1.14 tff(4079,plain,
% 0.97/1.14 ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) <=> (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4078])).
% 0.97/1.14 tff(4080,plain,
% 0.97/1.14 (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[2881, 102])).
% 0.97/1.14 tff(4081,plain,
% 0.97/1.14 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[97])).
% 0.97/1.14 tff(4082,plain,
% 0.97/1.14 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(z))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4081])).
% 0.97/1.14 tff(4083,plain,
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% 0.97/1.14 inference(modus_ponens,[status(thm)],[304, 4082])).
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[1402, 4084])).
% 0.97/1.14 tff(4086,plain,
% 0.97/1.14 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4051, 97])).
% 0.97/1.14 tff(4087,plain,
% 0.97/1.14 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4086])).
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[137, 112])).
% 0.97/1.14 tff(4090,plain,
% 0.97/1.14 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[2937, 4089])).
% 0.97/1.14 tff(4091,plain,
% 0.97/1.14 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[2981, 4090])).
% 0.97/1.14 tff(4092,plain,
% 0.97/1.14 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4052])).
% 0.97/1.14 tff(4093,plain,
% 0.97/1.14 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
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% 0.97/1.14 tff(4094,plain,
% 0.97/1.14 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[112])).
% 0.97/1.14 tff(4095,plain,
% 0.97/1.14 (b(s(s(s(elem!1))), z) <=> b(s(s(s(z))), elem!1)),
% 0.97/1.14 inference(transitivity,[status(thm)],[4094, 4093])).
% 0.97/1.14 tff(4096,plain,
% 0.97/1.14 (b(s(s(s(z))), elem!1)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[357, 4095])).
% 0.97/1.14 tff(4097,plain,
% 0.97/1.14 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4052, 97])).
% 0.97/1.14 tff(4098,plain,
% 0.97/1.14 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(z))), s(z))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4097])).
% 0.97/1.14 tff(4099,plain,
% 0.97/1.14 (r(s(s(s(z))), s(z))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[304, 4098])).
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% 0.97/1.14 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[2966, 4099, 102, 169, 4096])).
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[2578, 4100])).
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[3044, 4101, 4091, 4088, 4085, 3017])).
% 0.97/1.14 tff(4103,plain,
% 0.97/1.14 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[4102, 4079])).
% 0.97/1.14 tff(4104,plain,
% 0.97/1.14 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[97])).
% 0.97/1.14 tff(4105,plain,
% 0.97/1.14 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[4101, 4104])).
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% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(4107,plain,
% 0.97/1.14 (((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
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% 0.97/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4107])).
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% 0.97/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
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% 0.97/1.14 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
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% 0.97/1.14 inference(rewrite,[status(thm)],[])).
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% 0.97/1.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
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% 0.97/1.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[4114, 4113])).
% 0.97/1.14 tff(4116,plain,
% 0.97/1.14 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[4115, 150, 4112])).
% 0.97/1.14 tff(4117,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[4116, 4103, 4076])).
% 0.97/1.14 tff(4118,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~(s(z) = s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(z)), elem!1)) | (~r(z, s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
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% 0.97/1.14 inference(modus_ponens,[status(thm)],[4070, 4087])).
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[3515, 102])).
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% 0.97/1.14 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4052, 4051])).
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% 0.97/1.14 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
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% 0.97/1.14 inference(monotonicity,[status(thm)],[4125])).
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% 0.97/1.14 inference(monotonicity,[status(thm)],[4133])).
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% 0.97/1.14 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[1557, 4134])).
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% 0.97/1.14 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[3356, 4129, 102, 4080, 4122, 4121])).
% 0.97/1.14 tff(4137,plain,
% 0.97/1.14 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[1402, 4136])).
% 0.97/1.14 tff(4138,plain,
% 0.97/1.14 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[3385, 4137, 441, 4091, 4135, 4131])).
% 0.97/1.14 tff(4139,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[2377, 4138, 4132, 4050])).
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% 0.97/1.14 tff(4141,plain,
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[4140, 4027, 3889, 11, 4045, 4042])).
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[228, 4141])).
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% 0.97/1.14 (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[2881, 4028])).
% 0.97/1.14 tff(4144,plain,
% 0.97/1.14 (r(z, s(z)) <=> r(z, s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4027])).
% 0.97/1.14 tff(4145,plain,
% 0.97/1.14 (r(z, s(elem!1)) <=> r(z, s(z))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4144])).
% 0.97/1.14 tff(4146,plain,
% 0.97/1.14 (r(z, s(elem!1)) <=> r(elem!1, s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4029])).
% 0.97/1.14 tff(4147,plain,
% 0.97/1.14 (r(elem!1, s(elem!1)) <=> r(z, s(elem!1))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4146])).
% 0.97/1.14 tff(4148,plain,
% 0.97/1.14 (r(elem!1, s(elem!1)) <=> r(z, s(z))),
% 0.97/1.14 inference(transitivity,[status(thm)],[4147, 4145])).
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% 0.97/1.14 (r(elem!1, s(z)) <=> r(elem!1, s(elem!1))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4027])).
% 0.97/1.14 tff(4150,plain,
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% 0.97/1.14 inference(modus_ponens,[status(thm)],[3889, 4149])).
% 0.97/1.14 tff(4151,plain,
% 0.97/1.14 (r(z, s(z))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[4150, 4148])).
% 0.97/1.14 tff(4152,plain,
% 0.97/1.14 (~b(s(s(s(elem!1))), s(z))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[3580, 3160, 62, 65, 1606, 196, 11])).
% 0.97/1.14 tff(4153,plain,
% 0.97/1.14 (~r(s(s(s(elem!1))), s(z))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[493, 3161, 485])).
% 0.97/1.14 tff(4154,plain,
% 0.97/1.14 ($false),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[733, 4153, 4152])).
% 0.97/1.14 tff(4155,plain,(b(s(s(s(elem!1))), z) | (~r(z, s(z))) | b(s(elem!1), elem!1) | (elem!1 = s(z)) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.14 tff(4156,plain,
% 0.97/1.14 (b(s(s(s(elem!1))), z)),
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% 0.97/1.14 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(elem!1))), s(elem!1))),
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% 0.97/1.14 (b(s(s(s(elem!1))), s(elem!1)) <=> b(s(s(s(elem!1))), s(z))),
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% 0.97/1.14 tff(4159,plain,
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% 0.97/1.14 inference(modus_ponens,[status(thm)],[3889, 4062])).
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% 0.97/1.14 inference(modus_ponens,[status(thm)],[4159, 4061])).
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% 0.97/1.14 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[1611, 2793, 4160, 4080, 357])).
% 0.97/1.14 tff(4162,plain,
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[1402, 4161])).
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% 0.97/1.14 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = s(s(z)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4071])).
% 0.97/1.14 tff(4164,plain,
% 0.97/1.14 ((s(s(s(s(s(elem!1))))) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(s(elem!1)))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4163])).
% 0.97/1.14 tff(4165,plain,
% 0.97/1.14 ((~(s(s(s(s(s(elem!1))))) = s(s(z)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(elem!1))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4164])).
% 0.97/1.14 tff(4166,plain,
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% 0.97/1.14 inference(modus_ponens,[status(thm)],[2650, 4165])).
% 0.97/1.14 tff(4167,plain,
% 0.97/1.14 (r(s(z), elem!1) <=> r(s(elem!1), elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[97])).
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% 0.97/1.14 (r(s(elem!1), elem!1) <=> r(s(z), elem!1)),
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% 0.97/1.14 inference(modus_ponens,[status(thm)],[168, 4168])).
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% 0.97/1.14 inference(modus_ponens,[status(thm)],[294, 4098])).
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% 0.97/1.14 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[2966, 4170, 102, 4169, 4096])).
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[2578, 4171])).
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% 0.97/1.14 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[4172, 4104])).
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% 0.97/1.14 (~r(s(s(elem!1)), s(elem!1))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[333, 289, 58, 62, 11])).
% 0.97/1.14 tff(4175,plain,
% 0.97/1.14 (b(s(s(elem!1)), s(elem!1))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[605, 4174, 57])).
% 0.97/1.14 tff(4176,plain,
% 0.97/1.14 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 0.97/1.14 inference(monotonicity,[status(thm)],[112])).
% 0.97/1.14 tff(4177,plain,
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[139, 97, 62])).
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[283, 4177])).
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[4140, 97, 3889, 11, 4169, 4178])).
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% 0.97/1.14 inference(unit_resolution,[status(thm)],[228, 4179])).
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% 0.97/1.14 inference(modus_ponens,[status(thm)],[4180, 4176])).
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% 0.97/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(4183,plain,
% 0.97/1.14 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(4184,plain,
% 0.97/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4183])).
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% 0.97/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 0.97/1.14 inference(transitivity,[status(thm)],[4184, 4182])).
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% 0.97/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
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% 0.97/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[4186, 4185])).
% 0.97/1.14 tff(4188,plain,
% 0.97/1.14 (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[4187, 206, 4181, 4175, 4173])).
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% 0.97/1.14 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(4190,plain,
% 0.97/1.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(4191,plain,
% 0.97/1.14 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[4190, 4189])).
% 0.97/1.14 tff(4192,plain,
% 0.97/1.14 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[4191, 150, 4188])).
% 0.97/1.14 tff(4193,plain,
% 0.97/1.14 (r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[4192, 4166])).
% 0.97/1.14 tff(4194,plain,
% 0.97/1.14 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[4111, 206, 4175, 4173])).
% 0.97/1.14 tff(4195,plain,
% 0.97/1.14 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[4115, 150, 4194])).
% 0.97/1.14 tff(4196,plain,
% 0.97/1.14 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[4195, 4076])).
% 0.97/1.14 tff(4197,plain,
% 0.97/1.14 (b(s(s(s(elem!1))), elem!1)),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[357, 4094])).
% 0.97/1.14 tff(4198,plain,
% 0.97/1.14 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[573, 206, 4197, 4181])).
% 0.97/1.14 tff(4199,plain,
% 0.97/1.14 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[577, 150, 4198, 83])).
% 0.97/1.14 tff(4200,plain,
% 0.97/1.14 (b(z, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(elem!1))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[112])).
% 0.97/1.14 tff(4201,plain,
% 0.97/1.14 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(elem!1))))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4200])).
% 0.97/1.14 tff(4202,plain,
% 0.97/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(4203,plain,
% 0.97/1.14 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 0.97/1.14 inference(rewrite,[status(thm)],[])).
% 0.97/1.14 tff(4204,plain,
% 0.97/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4203])).
% 0.97/1.14 tff(4205,plain,
% 0.97/1.14 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 0.97/1.14 inference(transitivity,[status(thm)],[4204, 4202])).
% 0.97/1.14 tff(4206,plain,
% 0.97/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.97/1.14 inference(quant_inst,[status(thm)],[])).
% 0.97/1.14 tff(4207,plain,
% 0.97/1.14 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[4206, 4205])).
% 0.97/1.14 tff(4208,plain,
% 0.97/1.14 (~r(elem!1, s(s(s(elem!1))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[4207, 180, 4159, 294])).
% 0.97/1.14 tff(4209,plain,
% 0.97/1.14 (b(elem!1, s(s(s(elem!1))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[533, 4208, 419])).
% 0.97/1.14 tff(4210,plain,
% 0.97/1.14 (b(z, s(s(s(elem!1))))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[4209, 4201])).
% 0.97/1.14 tff(4211,plain,
% 0.97/1.14 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[3028, 4172, 1056])).
% 0.97/1.14 tff(4212,plain,
% 0.97/1.14 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.97/1.14 inference(unit_resolution,[status(thm)],[3033, 4211, 4091])).
% 0.97/1.14 tff(4213,plain,
% 0.97/1.14 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[4080, 1346])).
% 0.97/1.14 tff(4214,plain,
% 0.97/1.14 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(z)))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4071])).
% 0.97/1.14 tff(4215,plain,
% 0.97/1.14 ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.97/1.14 inference(symmetry,[status(thm)],[4214])).
% 0.97/1.14 tff(4216,plain,
% 0.97/1.14 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(z)))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4215])).
% 0.97/1.14 tff(4217,plain,
% 0.97/1.14 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.97/1.14 inference(modus_ponens,[status(thm)],[1111, 4216])).
% 0.97/1.14 tff(4218,plain,
% 0.97/1.14 (s(elem!1) = s(z)),
% 0.97/1.14 inference(symmetry,[status(thm)],[97])).
% 0.97/1.14 tff(4219,plain,
% 0.97/1.14 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.97/1.14 inference(monotonicity,[status(thm)],[4218])).
% 0.97/1.15 tff(4220,plain,
% 0.97/1.15 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.97/1.15 inference(symmetry,[status(thm)],[4219])).
% 0.97/1.15 tff(4221,plain,
% 0.97/1.15 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[1056, 4220])).
% 0.97/1.15 tff(4222,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4223,plain,
% 0.97/1.15 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4224,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4223])).
% 0.97/1.15 tff(4225,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.97/1.15 inference(transitivity,[status(thm)],[4224, 4222])).
% 0.97/1.15 tff(4226,plain,
% 0.97/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(4227,plain,
% 0.97/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[4226, 4225])).
% 0.97/1.15 tff(4228,plain,
% 0.97/1.15 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4227, 206, 4175, 4221])).
% 0.97/1.15 tff(4229,plain,
% 0.97/1.15 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4230,plain,
% 0.97/1.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(4231,plain,
% 0.97/1.15 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[4230, 4229])).
% 0.97/1.15 tff(4232,plain,
% 0.97/1.15 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4231, 150, 4228])).
% 0.97/1.15 tff(4233,plain,
% 0.97/1.15 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4232, 4217])).
% 0.97/1.15 tff(4234,plain,
% 0.97/1.15 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[327, 206, 4197, 4181])).
% 0.97/1.15 tff(4235,plain,
% 0.97/1.15 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[331, 150, 77, 4234])).
% 0.97/1.15 tff(4236,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4237,plain,
% 0.97/1.15 (((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4238,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4237])).
% 0.97/1.15 tff(4239,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.97/1.15 inference(transitivity,[status(thm)],[4238, 4236])).
% 0.97/1.15 tff(4240,plain,
% 0.97/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(4241,plain,
% 0.97/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[4240, 4239])).
% 0.97/1.15 tff(4242,plain,
% 0.97/1.15 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4241, 180, 294, 4235, 4233])).
% 0.97/1.15 tff(4243,plain,
% 0.97/1.15 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[1365, 4242, 4213])).
% 0.97/1.15 tff(4244,assumption,(~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.15 tff(4245,plain,
% 0.97/1.15 (z = elem!1),
% 0.97/1.15 inference(symmetry,[status(thm)],[121])).
% 0.97/1.15 tff(4246,plain,
% 0.97/1.15 (b(s(s(s(s(s(elem!1))))), z) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4245])).
% 0.97/1.15 tff(4247,plain,
% 0.97/1.15 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(s(s(s(elem!1))))), z)),
% 0.97/1.15 inference(symmetry,[status(thm)],[4246])).
% 0.97/1.15 tff(4248,plain,
% 0.97/1.15 ((z = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = z)),
% 0.97/1.15 inference(commutativity,[status(thm)],[])).
% 0.97/1.15 tff(4249,plain,
% 0.97/1.15 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (z = s(s(s(s(s(elem!1))))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[121])).
% 0.97/1.15 tff(4250,plain,
% 0.97/1.15 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = z)),
% 0.97/1.15 inference(transitivity,[status(thm)],[4249, 4248])).
% 0.97/1.15 tff(4251,plain,
% 0.97/1.15 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 0.97/1.15 inference(symmetry,[status(thm)],[4250])).
% 0.97/1.15 tff(4252,plain,
% 0.97/1.15 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 0.97/1.15 inference(transitivity,[status(thm)],[4251, 64])).
% 0.97/1.15 tff(4253,plain,
% 0.97/1.15 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4252])).
% 0.97/1.15 tff(4254,plain,
% 0.97/1.15 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[1395, 4253])).
% 0.97/1.15 tff(4255,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.97/1.15 tff(4256,plain,
% 0.97/1.15 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4245])).
% 0.97/1.15 tff(4257,plain,
% 0.97/1.15 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4256])).
% 0.97/1.15 tff(4258,plain,
% 0.97/1.15 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[1557, 4257])).
% 0.97/1.15 tff(4259,plain,
% 0.97/1.15 (b(s(s(s(s(s(s(elem!1)))))), z) <=> b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4245])).
% 0.97/1.15 tff(4260,plain,
% 0.97/1.15 ((~b(s(s(s(s(s(s(elem!1)))))), z)) <=> (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4259])).
% 0.97/1.15 tff(4261,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.15 tff(4262,assumption,(b(z, s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.15 tff(4263,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4264,plain,
% 0.97/1.15 (((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4265,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4264])).
% 0.97/1.15 tff(4266,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.97/1.15 inference(transitivity,[status(thm)],[4265, 4263])).
% 0.97/1.15 tff(4267,plain,
% 0.97/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(4268,plain,
% 0.97/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[4267, 4266])).
% 0.97/1.15 tff(4269,plain,
% 0.97/1.15 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4268, 206, 4262, 4261])).
% 0.97/1.15 tff(4270,plain,
% 0.97/1.15 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[4269, 4260])).
% 0.97/1.15 tff(4271,plain,
% 0.97/1.15 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[3090, 4270, 4258])).
% 0.97/1.15 tff(4272,plain,
% 0.97/1.15 (r(s(s(s(s(s(s(elem!1)))))), z) <=> r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4245])).
% 0.97/1.15 tff(4273,plain,
% 0.97/1.15 (r(s(s(s(s(s(s(elem!1)))))), elem!1) <=> r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.97/1.15 inference(symmetry,[status(thm)],[4272])).
% 0.97/1.15 tff(4274,assumption,(r(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 0.97/1.15 tff(4275,plain,
% 0.97/1.15 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[4274, 4273])).
% 0.97/1.15 tff(4276,plain,
% 0.97/1.15 (r(s(s(s(s(s(elem!1))))), z) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4245])).
% 0.97/1.15 tff(4277,plain,
% 0.97/1.15 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(s(s(s(elem!1))))), z)),
% 0.97/1.15 inference(symmetry,[status(thm)],[4276])).
% 0.97/1.15 tff(4278,plain,
% 0.97/1.15 (r(s(s(s(s(s(elem!1))))), z)),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[2948, 4277])).
% 0.97/1.15 tff(4279,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4280,plain,
% 0.97/1.15 (((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4281,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4280])).
% 0.97/1.15 tff(4282,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 0.97/1.15 inference(transitivity,[status(thm)],[4281, 4279])).
% 0.97/1.15 tff(4283,plain,
% 0.97/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(4284,plain,
% 0.97/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), z))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[4283, 4282])).
% 0.97/1.15 tff(4285,plain,
% 0.97/1.15 ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4284, 180, 4255])).
% 0.97/1.15 tff(4286,plain,
% 0.97/1.15 ($false),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4285, 4278, 4275])).
% 0.97/1.15 tff(4287,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~(elem!1 = z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.15 tff(4288,plain,
% 0.97/1.15 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4287, 4271, 121, 4255])).
% 0.97/1.15 tff(4289,plain,
% 0.97/1.15 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[2377, 4288, 4254])).
% 0.97/1.15 tff(4290,plain,
% 0.97/1.15 (b(s(s(s(s(s(elem!1))))), z)),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[4289, 4247])).
% 0.97/1.15 tff(4291,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4292,plain,
% 0.97/1.15 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4293,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4292])).
% 0.97/1.15 tff(4294,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 0.97/1.15 inference(transitivity,[status(thm)],[4293, 4291])).
% 0.97/1.15 tff(4295,plain,
% 0.97/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(4296,plain,
% 0.97/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[4295, 4294])).
% 0.97/1.15 tff(4297,plain,
% 0.97/1.15 ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4296, 206, 357])).
% 0.97/1.15 tff(4298,plain,
% 0.97/1.15 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4297, 4290])).
% 0.97/1.15 tff(4299,plain,
% 0.97/1.15 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[2431, 4298, 4244])).
% 0.97/1.15 tff(4300,plain,
% 0.97/1.15 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4299])).
% 0.97/1.15 tff(4301,plain,
% 0.97/1.15 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.97/1.15 inference(symmetry,[status(thm)],[4300])).
% 0.97/1.15 tff(4302,plain,
% 0.97/1.15 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[4261, 4301])).
% 0.97/1.15 tff(4303,assumption,(~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.97/1.15 tff(4304,plain,
% 0.97/1.15 ($false),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4303, 4302])).
% 0.97/1.15 tff(4305,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) | r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) | (~b(s(s(s(elem!1))), z)) | (~(elem!1 = z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.15 tff(4306,plain,
% 0.97/1.15 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4305, 4243, 357, 4211, 4089, 4212, 4210])).
% 0.97/1.15 tff(4307,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4308,plain,
% 0.97/1.15 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 0.97/1.15 inference(rewrite,[status(thm)],[])).
% 0.97/1.15 tff(4309,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 0.97/1.15 inference(monotonicity,[status(thm)],[4308])).
% 0.97/1.15 tff(4310,plain,
% 0.97/1.15 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 0.97/1.15 inference(transitivity,[status(thm)],[4309, 4307])).
% 0.97/1.15 tff(4311,plain,
% 0.97/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 0.97/1.15 inference(quant_inst,[status(thm)],[])).
% 0.97/1.15 tff(4312,plain,
% 0.97/1.15 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 0.97/1.15 inference(modus_ponens,[status(thm)],[4311, 4310])).
% 0.97/1.15 tff(4313,plain,
% 0.97/1.15 ($false),
% 0.97/1.15 inference(unit_resolution,[status(thm)],[4312, 180, 4306, 4199, 4196, 4193])).
% 0.97/1.15 tff(4314,plain,(b(s(s(s(elem!1))), s(elem!1)) | (~b(s(s(s(elem!1))), z)) | (~(s(z) = s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (s(s(s(elem!1))) = elem!1) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.16 tff(4315,plain,
% 0.97/1.16 (b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4314, 4162, 97, 357, 58, 62, 11])).
% 0.97/1.16 tff(4316,plain,
% 0.97/1.16 (b(s(s(s(elem!1))), s(z))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4315, 4158])).
% 0.97/1.16 tff(4317,plain,
% 0.97/1.16 ($false),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[728, 4316])).
% 0.97/1.16 tff(4318,plain,(b(s(s(s(elem!1))), s(z)) | (~(s(z) = s(elem!1))) | (~b(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = elem!1) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.16 tff(4319,plain,
% 0.97/1.16 (b(s(s(s(elem!1))), s(z))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4318, 4027, 4156, 58, 62, 11])).
% 0.97/1.16 tff(4320,plain,
% 0.97/1.16 (b(s(s(s(z))), s(z))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4319, 4040])).
% 0.97/1.16 tff(4321,plain,
% 0.97/1.16 (~(s(s(s(z))) = s(s(z)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[3515, 4028])).
% 0.97/1.16 tff(4322,plain,
% 0.97/1.16 (b(s(s(s(z))), s(s(z))) <=> b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4036, 4035])).
% 0.97/1.16 tff(4323,plain,
% 0.97/1.16 (b(s(s(s(elem!1))), s(s(elem!1))) <=> b(s(s(s(z))), s(s(z)))),
% 0.97/1.16 inference(symmetry,[status(thm)],[4322])).
% 0.97/1.16 tff(4324,plain,
% 0.97/1.16 ((~b(s(s(s(elem!1))), s(s(elem!1)))) <=> (~b(s(s(s(z))), s(s(z))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4323])).
% 0.97/1.16 tff(4325,plain,
% 0.97/1.16 (b(s(s(elem!1)), z) <=> b(s(s(elem!1)), elem!1)),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4029])).
% 0.97/1.16 tff(4326,plain,
% 0.97/1.16 (b(s(s(elem!1)), elem!1)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4142, 4325])).
% 0.97/1.16 tff(4327,plain,
% 0.97/1.16 (b(s(s(s(elem!1))), z) <=> b(s(s(s(elem!1))), elem!1)),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4029])).
% 0.97/1.16 tff(4328,plain,
% 0.97/1.16 (b(s(s(s(elem!1))), elem!1)),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4156, 4327])).
% 0.97/1.16 tff(4329,plain,
% 0.97/1.16 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[327, 206, 4328, 4326])).
% 0.97/1.16 tff(4330,plain,
% 0.97/1.16 (~b(s(s(s(z))), s(s(z)))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4329, 4324])).
% 0.97/1.16 tff(4331,plain,
% 0.97/1.16 (r(s(s(s(z))), s(s(z)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[1307, 4330, 4321])).
% 0.97/1.16 tff(4332,plain,
% 0.97/1.16 (elem!1 = z),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[137, 4029])).
% 0.97/1.16 tff(4333,plain,
% 0.97/1.16 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[2937, 4332])).
% 0.97/1.16 tff(4334,plain,
% 0.97/1.16 (b(s(s(z)), s(z)) <=> b(s(s(elem!1)), s(elem!1))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4035, 4027])).
% 0.97/1.16 tff(4335,plain,
% 0.97/1.16 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(z)), s(z))),
% 0.97/1.16 inference(symmetry,[status(thm)],[4334])).
% 0.97/1.16 tff(4336,plain,
% 0.97/1.16 (b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4319, 4039])).
% 0.97/1.16 tff(4337,plain,
% 0.97/1.16 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[82, 875])).
% 0.97/1.16 tff(4338,plain,
% 0.97/1.16 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[573, 206, 654, 2742])).
% 0.97/1.16 tff(4339,plain,
% 0.97/1.16 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[577, 150, 4338, 4337])).
% 0.97/1.16 tff(4340,plain,
% 0.97/1.16 (r(s(s(z)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4051, 97])).
% 0.97/1.16 tff(4341,plain,
% 0.97/1.16 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(z)), s(z))),
% 0.97/1.16 inference(symmetry,[status(thm)],[4340])).
% 0.97/1.16 tff(4342,plain,
% 0.97/1.16 (r(s(s(z)), s(z))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[254, 4341])).
% 0.97/1.16 tff(4343,plain,
% 0.97/1.16 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[3458, 4342, 102, 2742, 169])).
% 0.97/1.16 tff(4344,plain,
% 0.97/1.16 (b(s(s(s(s(s(elem!1))))), s(z))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[2578, 4343])).
% 0.97/1.16 tff(4345,plain,
% 0.97/1.16 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4344, 4104])).
% 0.97/1.16 tff(4346,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4347,plain,
% 0.97/1.16 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4348,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4347])).
% 0.97/1.16 tff(4349,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 0.97/1.16 inference(transitivity,[status(thm)],[4348, 4346])).
% 0.97/1.16 tff(4350,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(4351,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4350, 4349])).
% 0.97/1.16 tff(4352,plain,
% 0.97/1.16 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4351, 206, 654, 61, 4345])).
% 0.97/1.16 tff(4353,plain,
% 0.97/1.16 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[2431, 4352, 4090])).
% 0.97/1.16 tff(4354,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4355,plain,
% 0.97/1.16 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4356,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4355])).
% 0.97/1.16 tff(4357,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 0.97/1.16 inference(transitivity,[status(thm)],[4356, 4354])).
% 0.97/1.16 tff(4358,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(4359,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4358, 4357])).
% 0.97/1.16 tff(4360,plain,
% 0.97/1.16 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4359, 180, 4353, 254, 4339])).
% 0.97/1.16 tff(4361,plain,
% 0.97/1.16 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4191, 150, 4360])).
% 0.97/1.16 tff(4362,plain,
% 0.97/1.16 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4361, 4166])).
% 0.97/1.16 tff(4363,plain,
% 0.97/1.16 (~r(elem!1, s(s(elem!1)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[408, 180, 442, 254])).
% 0.97/1.16 tff(4364,plain,
% 0.97/1.16 (b(elem!1, s(s(elem!1)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[889, 4363, 27])).
% 0.97/1.16 tff(4365,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4366,plain,
% 0.97/1.16 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4367,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4366])).
% 0.97/1.16 tff(4368,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 0.97/1.16 inference(transitivity,[status(thm)],[4367, 4365])).
% 0.97/1.16 tff(4369,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(4370,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4369, 4368])).
% 0.97/1.16 tff(4371,plain,
% 0.97/1.16 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4370, 206, 4364, 4362])).
% 0.97/1.16 tff(4372,plain,
% 0.97/1.16 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[2377, 4371, 4050])).
% 0.97/1.16 tff(4373,plain,
% 0.97/1.16 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1)) <=> r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4218])).
% 0.97/1.16 tff(4374,plain,
% 0.97/1.16 ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4373])).
% 0.97/1.16 tff(4375,assumption,(s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.97/1.16 tff(4376,plain,
% 0.97/1.16 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 0.97/1.16 inference(symmetry,[status(thm)],[4375])).
% 0.97/1.16 tff(4377,plain,
% 0.97/1.16 (s(s(s(s(s(s(elem!1)))))) = s(s(z))),
% 0.97/1.16 inference(transitivity,[status(thm)],[4376, 4071])).
% 0.97/1.16 tff(4378,plain,
% 0.97/1.16 ($false),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[1111, 4377])).
% 0.97/1.16 tff(4379,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.16 tff(4380,plain,
% 0.97/1.16 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4379, 97])).
% 0.97/1.16 tff(4381,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(elem!1))), introduced(assumption)).
% 0.97/1.16 tff(4382,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4383,plain,
% 0.97/1.16 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4384,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4383])).
% 0.97/1.16 tff(4385,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.97/1.16 inference(transitivity,[status(thm)],[4384, 4382])).
% 0.97/1.16 tff(4386,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(4387,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4386, 4385])).
% 0.97/1.16 tff(4388,plain,
% 0.97/1.16 ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4387, 180, 442])).
% 0.97/1.16 tff(4389,plain,
% 0.97/1.16 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4388, 4381])).
% 0.97/1.16 tff(4390,plain,
% 0.97/1.16 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[3090, 4389, 3364])).
% 0.97/1.16 tff(4391,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4392,plain,
% 0.97/1.16 (((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4393,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4392])).
% 0.97/1.16 tff(4394,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.16 inference(transitivity,[status(thm)],[4393, 4391])).
% 0.97/1.16 tff(4395,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(4396,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4395, 4394])).
% 0.97/1.16 tff(4397,plain,
% 0.97/1.16 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4396, 206, 4390, 2742])).
% 0.97/1.16 tff(4398,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4399,plain,
% 0.97/1.16 (((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4400,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4399])).
% 0.97/1.16 tff(4401,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.16 inference(transitivity,[status(thm)],[4400, 4398])).
% 0.97/1.16 tff(4402,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(4403,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4402, 4401])).
% 0.97/1.16 tff(4404,plain,
% 0.97/1.16 ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4403, 180, 254])).
% 0.97/1.16 tff(4405,plain,
% 0.97/1.16 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4404, 4381])).
% 0.97/1.16 tff(4406,assumption,(~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.97/1.16 tff(4407,plain,
% 0.97/1.16 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4408,plain,
% 0.97/1.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(4409,plain,
% 0.97/1.16 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4408, 4407])).
% 0.97/1.16 tff(4410,plain,
% 0.97/1.16 ($false),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4409, 150, 4406, 4405, 4397])).
% 0.97/1.16 tff(4411,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.16 tff(4412,plain,
% 0.97/1.16 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4411, 254, 2742, 4135, 442, 4380])).
% 0.97/1.16 tff(4413,plain,
% 0.97/1.16 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4412, 4374])).
% 0.97/1.16 tff(4414,plain,
% 0.97/1.16 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[1402, 4413])).
% 0.97/1.16 tff(4415,plain,
% 0.97/1.16 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[3028, 4414, 4344])).
% 0.97/1.16 tff(4416,plain,
% 0.97/1.16 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[3033, 4415, 4091])).
% 0.97/1.16 tff(4417,plain,
% 0.97/1.16 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4287, 4416, 4089, 4372])).
% 0.97/1.16 tff(4418,plain,
% 0.97/1.16 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[3090, 4417, 4135])).
% 0.97/1.16 tff(4419,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4420,plain,
% 0.97/1.16 (((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.16 inference(rewrite,[status(thm)],[])).
% 0.97/1.16 tff(4421,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4420])).
% 0.97/1.16 tff(4422,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.16 inference(transitivity,[status(thm)],[4421, 4419])).
% 0.97/1.16 tff(4423,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.16 inference(quant_inst,[status(thm)],[])).
% 0.97/1.16 tff(4424,plain,
% 0.97/1.16 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4423, 4422])).
% 0.97/1.16 tff(4425,plain,
% 0.97/1.16 (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.97/1.16 inference(unit_resolution,[status(thm)],[4424, 206, 654, 4418])).
% 0.97/1.16 tff(4426,plain,
% 0.97/1.16 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 0.97/1.16 inference(symmetry,[status(thm)],[2921])).
% 0.97/1.16 tff(4427,plain,
% 0.97/1.16 ((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) <=> (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))))),
% 0.97/1.16 inference(monotonicity,[status(thm)],[4426])).
% 0.97/1.16 tff(4428,plain,
% 0.97/1.16 (~(s(s(s(elem!1))) = s(s(s(s(s(elem!1))))))),
% 0.97/1.16 inference(modus_ponens,[status(thm)],[4090, 4427])).
% 0.97/1.16 tff(4429,plain,
% 0.97/1.16 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4430,plain,
% 0.97/1.17 (((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4431,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[4430])).
% 0.97/1.17 tff(4432,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 0.97/1.17 inference(transitivity,[status(thm)],[4431, 4429])).
% 0.97/1.17 tff(4433,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(4434,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[4433, 4432])).
% 0.97/1.17 tff(4435,plain,
% 0.97/1.17 (~b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4434, 206, 61, 4345])).
% 0.97/1.17 tff(4436,plain,
% 0.97/1.17 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4437,plain,
% 0.97/1.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(4438,plain,
% 0.97/1.17 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[4437, 4436])).
% 0.97/1.17 tff(4439,plain,
% 0.97/1.17 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4438, 150, 4435])).
% 0.97/1.17 tff(4440,plain,
% 0.97/1.17 (r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4439, 4428])).
% 0.97/1.17 tff(4441,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4442,plain,
% 0.97/1.17 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4443,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[4442])).
% 0.97/1.17 tff(4444,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.17 inference(transitivity,[status(thm)],[4443, 4441])).
% 0.97/1.17 tff(4445,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(4446,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[4445, 4444])).
% 0.97/1.17 tff(4447,plain,
% 0.97/1.17 (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4446, 180, 4416, 4440])).
% 0.97/1.17 tff(4448,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[1088, 4447, 4425, 4080])).
% 0.97/1.17 tff(4449,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)) | (~(s(z) = s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~r(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(4450,plain,
% 0.97/1.17 (~r(s(s(elem!1)), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4449, 4328, 4027, 4326, 4150, 4336, 24, 4045])).
% 0.97/1.17 tff(4451,plain,
% 0.97/1.17 (b(s(s(elem!1)), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[605, 4450, 57])).
% 0.97/1.17 tff(4452,plain,
% 0.97/1.17 (b(s(s(z)), s(z))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[4451, 4335])).
% 0.97/1.17 tff(4453,plain,
% 0.97/1.17 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[3322, 4452, 4028, 4333, 4331, 4320])).
% 0.97/1.17 tff(4454,plain,
% 0.97/1.17 (r(s(s(s(s(s(elem!1))))), s(z))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[2578, 4453])).
% 0.97/1.17 tff(4455,plain,
% 0.97/1.17 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.97/1.17 inference(monotonicity,[status(thm)],[4029])).
% 0.97/1.17 tff(4456,plain,
% 0.97/1.17 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[4455])).
% 0.97/1.17 tff(4457,plain,
% 0.97/1.17 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[1557, 4456])).
% 0.97/1.17 tff(4458,plain,
% 0.97/1.17 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1))))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[2981, 4333])).
% 0.97/1.17 tff(4459,plain,
% 0.97/1.17 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[3356, 4452, 4028, 4143, 4331, 4320])).
% 0.97/1.17 tff(4460,plain,
% 0.97/1.17 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[1402, 4459])).
% 0.97/1.17 tff(4461,plain,
% 0.97/1.17 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[3385, 4460, 3889, 4458, 4457, 4454])).
% 0.97/1.17 tff(4462,plain,
% 0.97/1.17 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[3332, 4454, 3889])).
% 0.97/1.17 tff(4463,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[2377, 4462, 4461, 4034])).
% 0.97/1.17 tff(4464,plain,((elem!1 = s(z)) | (s(s(s(elem!1))) = elem!1) | b(s(elem!1), elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(4465,plain,
% 0.97/1.17 (elem!1 = s(z)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4464, 62, 58, 11])).
% 0.97/1.17 tff(4466,plain,
% 0.97/1.17 (r(s(elem!1), elem!1) <=> r(s(elem!1), s(z))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[4465])).
% 0.97/1.17 tff(4467,plain,
% 0.97/1.17 (r(s(elem!1), s(z)) <=> r(s(elem!1), elem!1)),
% 0.97/1.17 inference(symmetry,[status(thm)],[4466])).
% 0.97/1.17 tff(4468,plain,
% 0.97/1.17 ((~r(s(elem!1), s(z))) <=> (~r(s(elem!1), elem!1))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[4467])).
% 0.97/1.17 tff(4469,plain,
% 0.97/1.17 (~r(s(elem!1), elem!1)),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[3898, 4468])).
% 0.97/1.17 tff(4470,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[168, 4469])).
% 0.97/1.17 tff(4471,plain,(b(s(elem!1), elem!1) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(4472,plain,
% 0.97/1.17 (b(s(elem!1), elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4471, 58, 11])).
% 0.97/1.17 tff(4473,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4474,plain,
% 0.97/1.17 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4475,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[4474])).
% 0.97/1.17 tff(4476,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.97/1.17 inference(transitivity,[status(thm)],[4475, 4473])).
% 0.97/1.17 tff(4477,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(4478,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), elem!1))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[4477, 4476])).
% 0.97/1.17 tff(4479,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4478, 206, 1168, 654, 61])).
% 0.97/1.17 tff(4480,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(4481,plain,
% 0.97/1.17 (~b(s(s(s(elem!1))), elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4480, 61, 4472])).
% 0.97/1.17 tff(4482,plain,
% 0.97/1.17 (r(s(s(s(elem!1))), elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[320, 4481, 58])).
% 0.97/1.17 tff(4483,plain,
% 0.97/1.17 (~r(elem!1, z)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[382, 4482, 60])).
% 0.97/1.17 tff(4484,plain,
% 0.97/1.17 (b(elem!1, z)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[387, 4483, 2794])).
% 0.97/1.17 tff(4485,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4486,plain,
% 0.97/1.17 (((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4487,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[4486])).
% 0.97/1.17 tff(4488,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)))),
% 0.97/1.17 inference(transitivity,[status(thm)],[4487, 4485])).
% 0.97/1.17 tff(4489,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(4490,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[4489, 4488])).
% 0.97/1.17 tff(4491,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4490, 206, 1168, 653, 95])).
% 0.97/1.17 tff(4492,plain,((~b(elem!1, z)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(4493,plain,
% 0.97/1.17 (~b(s(elem!1), z)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4492, 4484, 4472])).
% 0.97/1.17 tff(4494,plain,
% 0.97/1.17 (r(s(elem!1), z)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[283, 4493])).
% 0.97/1.17 tff(4495,plain,
% 0.97/1.17 (~r(s(s(elem!1)), z)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[3976, 4494, 11, 60])).
% 0.97/1.17 tff(4496,plain,
% 0.97/1.17 (b(s(s(elem!1)), z)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[228, 4495])).
% 0.97/1.17 tff(4497,plain,
% 0.97/1.17 (~b(elem!1, s(s(elem!1)))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[2809, 206, 4484, 4496])).
% 0.97/1.17 tff(4498,plain,
% 0.97/1.17 (r(elem!1, s(s(elem!1)))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[889, 4497, 24])).
% 0.97/1.17 tff(4499,plain,
% 0.97/1.17 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[673, 4498, 4482])).
% 0.97/1.17 tff(4500,plain,
% 0.97/1.17 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[331, 150, 77, 4499])).
% 0.97/1.17 tff(4501,plain,
% 0.97/1.17 (~b(s(s(elem!1)), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[640, 4500, 61])).
% 0.97/1.17 tff(4502,plain,
% 0.97/1.17 (r(s(s(elem!1)), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[605, 4501, 57])).
% 0.97/1.17 tff(4503,plain,
% 0.97/1.17 (b(elem!1, s(z))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[3732, 4481, 58, 2794, 11])).
% 0.97/1.17 tff(4504,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[917, 206, 653, 157, 911])).
% 0.97/1.17 tff(4505,plain,((~b(z, s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(4506,plain,
% 0.97/1.17 (~b(z, s(z))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4505, 4484, 4503])).
% 0.97/1.17 tff(4507,plain,
% 0.97/1.17 (r(z, s(z))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[505, 4506])).
% 0.97/1.17 tff(4508,plain,
% 0.97/1.17 (~r(s(s(s(elem!1))), s(z))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[493, 4507, 60])).
% 0.97/1.17 tff(4509,plain,
% 0.97/1.17 (b(s(s(s(elem!1))), s(z))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[733, 4508])).
% 0.97/1.17 tff(4510,plain,
% 0.97/1.17 (~b(s(z), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[907, 4509, 61])).
% 0.97/1.17 tff(4511,plain,
% 0.97/1.17 (r(s(z), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[467, 4510, 59])).
% 0.97/1.17 tff(4512,plain,
% 0.97/1.17 (~b(s(s(elem!1)), s(z))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[892, 4509, 58, 4503, 4496, 24])).
% 0.97/1.17 tff(4513,plain,
% 0.97/1.17 (r(s(s(elem!1)), s(z))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[778, 4512])).
% 0.97/1.17 tff(4514,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[858, 4513, 4511, 4502])).
% 0.97/1.17 tff(4515,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(4516,plain,
% 0.97/1.17 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4515, 60, 58, 59, 11])).
% 0.97/1.17 tff(4517,plain,
% 0.97/1.17 (~r(s(elem!1), z)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[1176, 294, 60])).
% 0.97/1.17 tff(4518,plain,
% 0.97/1.17 (b(s(elem!1), z)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[283, 4517])).
% 0.97/1.17 tff(4519,plain,
% 0.97/1.17 (~b(elem!1, z)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4492, 4518, 4472])).
% 0.97/1.17 tff(4520,plain,
% 0.97/1.17 (r(elem!1, z)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[387, 4519, 2794])).
% 0.97/1.17 tff(4521,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4522,plain,
% 0.97/1.17 (((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1)))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4523,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[4522])).
% 0.97/1.17 tff(4524,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z)))),
% 0.97/1.17 inference(transitivity,[status(thm)],[4523, 4521])).
% 0.97/1.17 tff(4525,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), z)) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(4526,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), z))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[4525, 4524])).
% 0.97/1.17 tff(4527,plain,
% 0.97/1.17 (~r(elem!1, s(s(s(elem!1))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4526, 180, 4520, 60])).
% 0.97/1.17 tff(4528,plain,
% 0.97/1.17 (b(elem!1, s(s(s(elem!1))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[533, 4527, 419])).
% 0.97/1.17 tff(4529,plain,
% 0.97/1.17 (~b(z, elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[1188, 4518, 4472])).
% 0.97/1.17 tff(4530,plain,
% 0.97/1.17 (r(z, elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[556, 4529, 910])).
% 0.97/1.17 tff(4531,plain,
% 0.97/1.17 (~r(s(s(s(elem!1))), elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[1192, 289, 60, 910, 11])).
% 0.97/1.17 tff(4532,plain,
% 0.97/1.17 (b(s(s(s(elem!1))), elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[320, 4531, 58])).
% 0.97/1.17 tff(4533,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4534,plain,
% 0.97/1.17 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4535,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[4534])).
% 0.97/1.17 tff(4536,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1)))),
% 0.97/1.17 inference(transitivity,[status(thm)],[4535, 4533])).
% 0.97/1.17 tff(4537,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(4538,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), elem!1))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[4537, 4536])).
% 0.97/1.17 tff(4539,plain,
% 0.97/1.17 ($false),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4538, 206, 1168, 654, 356])).
% 0.97/1.17 tff(4540,plain,((~b(s(s(s(elem!1))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.17 tff(4541,plain,
% 0.97/1.17 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4540, 4532, 4472])).
% 0.97/1.17 tff(4542,plain,
% 0.97/1.17 (r(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[354, 4541, 18])).
% 0.97/1.17 tff(4543,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 0.97/1.17 tff(4544,plain,
% 0.97/1.17 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[82, 80])).
% 0.97/1.17 tff(4545,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4546,plain,
% 0.97/1.17 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4547,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[4546])).
% 0.97/1.17 tff(4548,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.17 inference(transitivity,[status(thm)],[4547, 4545])).
% 0.97/1.17 tff(4549,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(4550,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[4549, 4548])).
% 0.97/1.17 tff(4551,plain,
% 0.97/1.17 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4550, 180, 60, 304, 254])).
% 0.97/1.17 tff(4552,plain,
% 0.97/1.17 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[577, 150, 4551, 4544])).
% 0.97/1.17 tff(4553,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.17 tff(4554,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4555,plain,
% 0.97/1.17 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.17 inference(rewrite,[status(thm)],[])).
% 0.97/1.17 tff(4556,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.97/1.17 inference(monotonicity,[status(thm)],[4555])).
% 0.97/1.17 tff(4557,plain,
% 0.97/1.17 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.17 inference(transitivity,[status(thm)],[4556, 4554])).
% 0.97/1.17 tff(4558,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 0.97/1.17 inference(quant_inst,[status(thm)],[])).
% 0.97/1.17 tff(4559,plain,
% 0.97/1.17 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.97/1.17 inference(modus_ponens,[status(thm)],[4558, 4557])).
% 0.97/1.17 tff(4560,plain,
% 0.97/1.17 (~b(s(s(elem!1)), elem!1)),
% 0.97/1.17 inference(unit_resolution,[status(thm)],[4559, 206, 4553, 4552])).
% 0.97/1.18 tff(4561,plain,
% 0.97/1.18 (r(s(s(elem!1)), elem!1)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[267, 150, 4560, 4543])).
% 0.97/1.18 tff(4562,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.97/1.18 tff(4563,plain,
% 0.97/1.18 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[300, 180, 304, 254])).
% 0.97/1.18 tff(4564,plain,
% 0.97/1.18 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[331, 150, 80, 4563])).
% 0.97/1.18 tff(4565,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4566,plain,
% 0.97/1.18 (((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4567,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4566])).
% 0.97/1.18 tff(4568,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 0.97/1.18 inference(transitivity,[status(thm)],[4567, 4565])).
% 0.97/1.18 tff(4569,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, s(s(elem!1)))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(4570,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4569, 4568])).
% 0.97/1.18 tff(4571,plain,
% 0.97/1.18 (~r(z, s(s(elem!1)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4570, 180, 543, 4561])).
% 0.97/1.18 tff(4572,plain,
% 0.97/1.18 (b(z, s(s(elem!1)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[2185, 4571])).
% 0.97/1.18 tff(4573,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4574,plain,
% 0.97/1.18 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4575,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4574])).
% 0.97/1.18 tff(4576,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 0.97/1.18 inference(transitivity,[status(thm)],[4575, 4573])).
% 0.97/1.18 tff(4577,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(4578,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(z, s(s(s(elem!1))))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(elem!1))))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4577, 4576])).
% 0.97/1.18 tff(4579,plain,
% 0.97/1.18 (~b(z, s(s(s(elem!1))))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4578, 206, 654, 4572, 4564])).
% 0.97/1.18 tff(4580,plain,
% 0.97/1.18 (r(z, s(s(s(elem!1))))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[1985, 4579])).
% 0.97/1.18 tff(4581,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4582,plain,
% 0.97/1.18 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1)))) <=> ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4583,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1)))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4582])).
% 0.97/1.18 tff(4584,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))))),
% 0.97/1.18 inference(transitivity,[status(thm)],[4583, 4581])).
% 0.97/1.18 tff(4585,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(4586,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, s(elem!1)))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4585, 4584])).
% 0.97/1.18 tff(4587,plain,
% 0.97/1.18 (~r(z, s(elem!1))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4586, 180, 4580, 4562])).
% 0.97/1.18 tff(4588,plain,
% 0.97/1.18 (b(z, s(elem!1))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[817, 150, 4587, 235])).
% 0.97/1.18 tff(4589,plain,
% 0.97/1.18 (~r(z, s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[493, 243, 60])).
% 0.97/1.18 tff(4590,plain,
% 0.97/1.18 (b(z, s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[505, 4589])).
% 0.97/1.18 tff(4591,plain,
% 0.97/1.18 (~r(s(z), s(elem!1))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[436, 243, 304])).
% 0.97/1.18 tff(4592,plain,
% 0.97/1.18 (b(s(z), s(elem!1))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[467, 4591, 59])).
% 0.97/1.18 tff(4593,plain,
% 0.97/1.18 ($false),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[951, 4592, 4590, 943])).
% 0.97/1.18 tff(4594,plain,((~r(s(s(s(elem!1))), s(z))) | (~b(z, s(elem!1))) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.18 tff(4595,plain,
% 0.97/1.18 (~r(s(s(s(elem!1))), s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4594, 4588, 59, 304, 60])).
% 0.97/1.18 tff(4596,plain,
% 0.97/1.18 (b(s(s(s(elem!1))), s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[733, 4595])).
% 0.97/1.18 tff(4597,plain,
% 0.97/1.18 (~b(s(s(elem!1)), s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[759, 4596, 4552])).
% 0.97/1.18 tff(4598,plain,
% 0.97/1.18 (r(s(s(elem!1)), s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[778, 4597])).
% 0.97/1.18 tff(4599,plain,
% 0.97/1.18 (~b(elem!1, s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[743, 4596, 654])).
% 0.97/1.18 tff(4600,plain,
% 0.97/1.18 (r(elem!1, s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[154, 4599, 65])).
% 0.97/1.18 tff(4601,plain,
% 0.97/1.18 ($false),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[3694, 4600, 4598, 4561])).
% 0.97/1.18 tff(4602,plain,((~r(s(s(elem!1)), s(elem!1))) | (elem!1 = s(z)) | (~b(s(s(s(elem!1))), elem!1)) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(z, elem!1)) | (s(s(elem!1)) = elem!1) | (~b(elem!1, s(s(s(elem!1))))) | (s(s(s(elem!1))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.18 tff(4603,plain,
% 0.97/1.18 (~r(s(s(elem!1)), s(elem!1))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4602, 4532, 65, 59, 294, 60, 4542, 4530, 30, 4528, 77])).
% 0.97/1.18 tff(4604,plain,
% 0.97/1.18 (b(s(s(elem!1)), s(elem!1))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[605, 4603, 57])).
% 0.97/1.18 tff(4605,plain,
% 0.97/1.18 (~b(s(s(elem!1)), z)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[214, 4604, 4518])).
% 0.97/1.18 tff(4606,plain,
% 0.97/1.18 (r(s(s(elem!1)), z)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[228, 4605])).
% 0.97/1.18 tff(4607,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4608,plain,
% 0.97/1.18 (((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4609,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4608])).
% 0.97/1.18 tff(4610,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 0.97/1.18 inference(transitivity,[status(thm)],[4609, 4607])).
% 0.97/1.18 tff(4611,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(4612,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1))))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4611, 4610])).
% 0.97/1.18 tff(4613,plain,
% 0.97/1.18 (~r(elem!1, s(s(elem!1)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4612, 180, 4520, 4606])).
% 0.97/1.18 tff(4614,plain,
% 0.97/1.18 (~b(s(s(elem!1)), s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[615, 607, 195])).
% 0.97/1.18 tff(4615,plain,
% 0.97/1.18 (r(s(s(elem!1)), s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[778, 4614])).
% 0.97/1.18 tff(4616,plain,
% 0.97/1.18 (~r(s(z), z)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[789, 4615, 241])).
% 0.97/1.18 tff(4617,plain,
% 0.97/1.18 (b(s(z), z)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[794, 4616])).
% 0.97/1.18 tff(4618,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4619,plain,
% 0.97/1.18 (((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4620,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4619])).
% 0.97/1.18 tff(4621,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 0.97/1.18 inference(transitivity,[status(thm)],[4620, 4618])).
% 0.97/1.18 tff(4622,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(4623,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4622, 4621])).
% 0.97/1.18 tff(4624,plain,
% 0.97/1.18 ($false),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4623, 206, 1168, 95, 4617, 607])).
% 0.97/1.18 tff(4625,plain,((~b(s(z), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.18 tff(4626,plain,
% 0.97/1.18 (~b(s(z), s(elem!1))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4625, 4606, 4518, 4604, 4472])).
% 0.97/1.18 tff(4627,plain,
% 0.97/1.18 (r(s(z), s(elem!1))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[467, 4626, 59])).
% 0.97/1.18 tff(4628,plain,
% 0.97/1.18 (~r(s(s(s(elem!1))), s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[436, 4627, 294])).
% 0.97/1.18 tff(4629,plain,
% 0.97/1.18 (b(s(s(s(elem!1))), s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[733, 4628])).
% 0.97/1.18 tff(4630,plain,
% 0.97/1.18 (~b(elem!1, s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[743, 4629, 4532])).
% 0.97/1.18 tff(4631,plain,
% 0.97/1.18 (r(elem!1, s(z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[154, 4630, 65])).
% 0.97/1.18 tff(4632,plain,
% 0.97/1.18 (~r(elem!1, s(elem!1))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[450, 4631, 4627])).
% 0.97/1.18 tff(4633,plain,
% 0.97/1.18 (b(elem!1, s(elem!1))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[401, 4632, 46])).
% 0.97/1.18 tff(4634,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4635,plain,
% 0.97/1.18 (((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4636,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4635])).
% 0.97/1.18 tff(4637,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 0.97/1.18 inference(transitivity,[status(thm)],[4636, 4634])).
% 0.97/1.18 tff(4638,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1)))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(4639,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(s(elem!1))))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4638, 4637])).
% 0.97/1.18 tff(4640,plain,
% 0.97/1.18 (~b(elem!1, s(s(elem!1)))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4639, 206, 4633, 4604])).
% 0.97/1.18 tff(4641,plain,
% 0.97/1.18 ($false),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[889, 4640, 4613, 24])).
% 0.97/1.18 tff(4642,plain,(b(s(s(s(elem!1))), s(elem!1)) | (elem!1 = s(z)) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.18 tff(4643,plain,
% 0.97/1.18 (elem!1 = s(z)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4642, 4516, 59, 60, 58, 11])).
% 0.97/1.18 tff(4644,plain,
% 0.97/1.18 (s(elem!1) = s(s(z))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4643])).
% 0.97/1.18 tff(4645,plain,
% 0.97/1.18 (s(s(elem!1)) = s(s(s(z)))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4644])).
% 0.97/1.18 tff(4646,plain,
% 0.97/1.18 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4645])).
% 0.97/1.18 tff(4647,plain,
% 0.97/1.18 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4645, 4646])).
% 0.97/1.18 tff(4648,plain,
% 0.97/1.18 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.18 inference(symmetry,[status(thm)],[4647])).
% 0.97/1.18 tff(4649,plain,
% 0.97/1.18 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[1295, 4643])).
% 0.97/1.18 tff(4650,plain,
% 0.97/1.18 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[2467, 4649])).
% 0.97/1.18 tff(4651,plain,
% 0.97/1.18 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 0.97/1.18 inference(symmetry,[status(thm)],[4646])).
% 0.97/1.18 tff(4652,plain,
% 0.97/1.18 (r(s(s(s(s(z)))), z) <=> r(s(s(s(elem!1))), z)),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4651])).
% 0.97/1.18 tff(4653,plain,
% 0.97/1.18 (r(s(s(s(elem!1))), z) <=> r(s(s(s(s(z)))), z)),
% 0.97/1.18 inference(symmetry,[status(thm)],[4652])).
% 0.97/1.18 tff(4654,plain,
% 0.97/1.18 (r(s(s(s(s(z)))), z)),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[60, 4653])).
% 0.97/1.18 tff(4655,plain,
% 0.97/1.18 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4651])).
% 0.97/1.18 tff(4656,plain,
% 0.97/1.18 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 0.97/1.18 inference(symmetry,[status(thm)],[4655])).
% 0.97/1.18 tff(4657,plain,
% 0.97/1.18 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4644])).
% 0.97/1.18 tff(4658,plain,
% 0.97/1.18 (r(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[293, 4516, 11])).
% 0.97/1.18 tff(4659,plain,
% 0.97/1.18 (r(s(s(s(elem!1))), s(s(z)))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4658, 4657])).
% 0.97/1.18 tff(4660,plain,
% 0.97/1.18 (r(s(s(s(s(z)))), s(s(z)))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4659, 4656])).
% 0.97/1.18 tff(4661,plain,
% 0.97/1.18 (r(s(s(elem!1)), z) <=> r(s(s(s(z))), z)),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4645])).
% 0.97/1.18 tff(4662,plain,
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% 0.97/1.18 inference(unit_resolution,[status(thm)],[1176, 4658, 60])).
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% 0.97/1.18 inference(unit_resolution,[status(thm)],[283, 4662])).
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% 0.97/1.18 (b(elem!1, s(s(s(elem!1)))) <=> b(s(z), s(s(s(s(z)))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4643, 4646])).
% 0.97/1.18 tff(4665,plain,
% 0.97/1.18 (r(elem!1, s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4643])).
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% 0.97/1.18 (r(s(z), s(s(s(elem!1)))) <=> r(elem!1, s(s(s(elem!1))))),
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% 0.97/1.18 tff(4667,plain,
% 0.97/1.18 (r(s(z), s(s(s(s(z))))) <=> r(s(z), s(s(s(elem!1))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4651])).
% 0.97/1.18 tff(4668,plain,
% 0.97/1.18 (r(s(z), s(s(s(s(z))))) <=> r(elem!1, s(s(s(elem!1))))),
% 0.97/1.18 inference(transitivity,[status(thm)],[4667, 4666])).
% 0.97/1.18 tff(4669,plain,
% 0.97/1.18 ((~r(s(z), s(s(s(s(z)))))) <=> (~r(elem!1, s(s(s(elem!1)))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4668])).
% 0.97/1.18 tff(4670,plain,
% 0.97/1.18 (r(elem!1, z) <=> r(s(z), z)),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4643])).
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% 0.97/1.18 inference(unit_resolution,[status(thm)],[4492, 4663, 4472])).
% 0.97/1.18 tff(4672,plain,
% 0.97/1.18 (r(elem!1, z)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[387, 4671, 2794])).
% 0.97/1.18 tff(4673,plain,
% 0.97/1.18 (r(s(z), z)),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4672, 4670])).
% 0.97/1.18 tff(4674,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4675,plain,
% 0.97/1.18 (((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z))))))) <=> ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4676,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4675])).
% 0.97/1.18 tff(4677,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.97/1.18 inference(transitivity,[status(thm)],[4676, 4674])).
% 0.97/1.18 tff(4678,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))))),
% 0.97/1.18 inference(quant_inst,[status(thm)],[])).
% 0.97/1.18 tff(4679,plain,
% 0.97/1.18 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4678, 4677])).
% 0.97/1.18 tff(4680,plain,
% 0.97/1.18 ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4679, 180, 4673, 4660])).
% 0.97/1.18 tff(4681,plain,
% 0.97/1.18 (~r(s(z), s(s(s(s(z)))))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4680, 4654])).
% 0.97/1.18 tff(4682,plain,
% 0.97/1.18 (~r(elem!1, s(s(s(elem!1))))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4681, 4669])).
% 0.97/1.18 tff(4683,plain,
% 0.97/1.18 (b(elem!1, s(s(s(elem!1))))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[533, 4682, 419])).
% 0.97/1.18 tff(4684,plain,
% 0.97/1.18 (b(s(z), s(s(s(s(z)))))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4683, 4664])).
% 0.97/1.18 tff(4685,plain,
% 0.97/1.18 (~r(s(s(s(elem!1))), elem!1)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[1192, 4516, 60, 910, 11])).
% 0.97/1.18 tff(4686,plain,
% 0.97/1.18 (b(s(s(s(elem!1))), elem!1)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[320, 4685, 58])).
% 0.97/1.18 tff(4687,plain,
% 0.97/1.18 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[4540, 4686, 4472])).
% 0.97/1.18 tff(4688,plain,
% 0.97/1.18 (r(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[354, 4687, 18])).
% 0.97/1.18 tff(4689,plain,
% 0.97/1.18 (r(z, elem!1) <=> r(z, s(z))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4643])).
% 0.97/1.18 tff(4690,plain,
% 0.97/1.18 (~b(z, elem!1)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[1188, 4663, 4472])).
% 0.97/1.18 tff(4691,plain,
% 0.97/1.18 (r(z, elem!1)),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[556, 4690, 910])).
% 0.97/1.18 tff(4692,plain,
% 0.97/1.18 (r(z, s(z))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4691, 4689])).
% 0.97/1.18 tff(4693,plain,
% 0.97/1.18 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4644])).
% 0.97/1.18 tff(4694,plain,
% 0.97/1.18 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4643])).
% 0.97/1.18 tff(4695,plain,
% 0.97/1.18 (b(s(elem!1), s(z))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4472, 4694])).
% 0.97/1.18 tff(4696,plain,
% 0.97/1.18 (b(s(s(z)), s(z))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4695, 4693])).
% 0.97/1.18 tff(4697,plain,
% 0.97/1.18 (s(z) = elem!1),
% 0.97/1.18 inference(symmetry,[status(thm)],[4643])).
% 0.97/1.18 tff(4698,plain,
% 0.97/1.18 (b(s(s(s(s(z)))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4697])).
% 0.97/1.18 tff(4699,plain,
% 0.97/1.18 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(z))),
% 0.97/1.18 inference(symmetry,[status(thm)],[4698])).
% 0.97/1.18 tff(4700,plain,
% 0.97/1.18 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4651, 4643])).
% 0.97/1.18 tff(4701,plain,
% 0.97/1.18 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), elem!1)),
% 0.97/1.18 inference(symmetry,[status(thm)],[4700])).
% 0.97/1.18 tff(4702,plain,
% 0.97/1.18 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 0.97/1.18 inference(monotonicity,[status(thm)],[4643])).
% 0.97/1.18 tff(4703,plain,
% 0.97/1.18 (b(s(s(s(elem!1))), s(z))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4686, 4702])).
% 0.97/1.18 tff(4704,plain,
% 0.97/1.18 (b(s(s(s(s(z)))), elem!1)),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4703, 4701])).
% 0.97/1.18 tff(4705,plain,
% 0.97/1.18 (b(s(s(s(s(z)))), s(z))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4704, 4699])).
% 0.97/1.18 tff(4706,plain,
% 0.97/1.18 (r(s(s(elem!1)), s(elem!1))),
% 0.97/1.18 inference(unit_resolution,[status(thm)],[605, 897, 74])).
% 0.97/1.18 tff(4707,plain,
% 0.97/1.18 (r(s(s(s(z))), s(s(z)))),
% 0.97/1.18 inference(modus_ponens,[status(thm)],[4706, 2442])).
% 0.97/1.18 tff(4708,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4709,plain,
% 0.97/1.18 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.97/1.18 inference(rewrite,[status(thm)],[])).
% 0.97/1.18 tff(4710,plain,
% 0.97/1.18 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[4709])).
% 0.97/1.19 tff(4711,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.97/1.19 inference(transitivity,[status(thm)],[4710, 4708])).
% 0.97/1.19 tff(4712,plain,
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% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(4713,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4712, 4711])).
% 0.97/1.19 tff(4714,plain,
% 0.97/1.19 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4713, 180, 4707, 1691])).
% 0.97/1.19 tff(4715,plain,
% 0.97/1.19 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2471, 150, 4714, 2468])).
% 0.97/1.19 tff(4716,plain,
% 0.97/1.19 (~b(s(s(s(z))), s(z))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2560, 206, 2565, 4715])).
% 0.97/1.19 tff(4717,plain,
% 0.97/1.19 (r(s(s(s(z))), s(z))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[1865, 4716, 1721])).
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% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4719,plain,
% 0.97/1.19 (((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4720,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[4719])).
% 0.97/1.19 tff(4721,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 0.97/1.19 inference(transitivity,[status(thm)],[4720, 4718])).
% 0.97/1.19 tff(4722,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(z, s(s(s(z))))))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(4723,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(z)))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4722, 4721])).
% 0.97/1.19 tff(4724,plain,
% 0.97/1.19 (~r(z, s(s(s(z))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4723, 180, 485, 4717])).
% 0.97/1.19 tff(4725,plain,
% 0.97/1.19 (~r(z, s(s(elem!1)))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4724, 2166])).
% 0.97/1.19 tff(4726,plain,
% 0.97/1.19 (b(z, s(s(elem!1)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2185, 4725])).
% 0.97/1.19 tff(4727,plain,
% 0.97/1.19 (b(z, s(s(s(z))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4726, 2163])).
% 0.97/1.19 tff(4728,plain,
% 0.97/1.19 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[1708, 180, 4707, 1691])).
% 0.97/1.19 tff(4729,plain,
% 0.97/1.19 (b(s(s(s(s(z)))), s(s(s(z))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[1299, 150, 1296, 4728])).
% 0.97/1.19 tff(4730,assumption,(b(s(s(s(s(z)))), s(z))), introduced(assumption)).
% 0.97/1.19 tff(4731,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4732,plain,
% 0.97/1.19 (((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4733,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[4732])).
% 0.97/1.19 tff(4734,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 0.97/1.19 inference(transitivity,[status(thm)],[4733, 4731])).
% 0.97/1.19 tff(4735,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z)))))))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(4736,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(s(z))))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(s(s(s(z))))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4735, 4734])).
% 0.97/1.19 tff(4737,plain,
% 0.97/1.19 (~b(z, s(s(s(s(z)))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4736, 206, 4730, 4729, 4727])).
% 0.97/1.19 tff(4738,plain,
% 0.97/1.19 (~b(z, s(s(s(elem!1))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4737, 2656])).
% 0.97/1.19 tff(4739,plain,
% 0.97/1.19 (r(z, s(s(s(elem!1))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[1985, 4738])).
% 0.97/1.19 tff(4740,plain,
% 0.97/1.19 (r(z, s(s(s(s(z)))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4739, 2655])).
% 0.97/1.19 tff(4741,plain,
% 0.97/1.19 (b(s(s(s(z))), z)),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[196, 1014])).
% 0.97/1.19 tff(4742,assumption,(r(z, s(s(s(s(z)))))), introduced(assumption)).
% 0.97/1.19 tff(4743,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4744,plain,
% 0.97/1.19 (((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4745,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[4744])).
% 0.97/1.19 tff(4746,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 0.97/1.19 inference(transitivity,[status(thm)],[4745, 4743])).
% 0.97/1.19 tff(4747,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(4748,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4747, 4746])).
% 0.97/1.19 tff(4749,plain,
% 0.97/1.19 (~r(s(s(s(s(s(elem!1))))), z)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4748, 180, 2580, 485, 4742])).
% 0.97/1.19 tff(4750,plain,
% 0.97/1.19 (b(s(s(s(s(s(elem!1))))), z)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2388, 150, 1395, 4749])).
% 0.97/1.19 tff(4751,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 0.97/1.19 tff(4752,plain,
% 0.97/1.19 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2455, 150, 2940, 2563])).
% 0.97/1.19 tff(4753,plain,
% 0.97/1.19 ($false),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[3886, 206, 4752, 4751, 4750])).
% 0.97/1.19 tff(4754,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(z))), z)) | (s(s(s(z))) = s(s(s(s(s(elem!1)))))) | (~r(z, s(z))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.19 tff(4755,plain,
% 0.97/1.19 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4754, 4741, 2440, 485, 4740, 4717])).
% 0.97/1.19 tff(4756,plain,
% 0.97/1.19 (b(s(s(s(s(s(elem!1))))), s(z))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2578, 4755])).
% 0.97/1.19 tff(4757,plain,
% 0.97/1.19 (~b(s(s(s(s(s(elem!1))))), s(s(z)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[3057, 206, 4756, 1694])).
% 0.97/1.19 tff(4758,plain,
% 0.97/1.19 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2653, 150, 2650, 4757])).
% 0.97/1.19 tff(4759,plain,
% 0.97/1.19 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[1003])).
% 0.97/1.19 tff(4760,plain,
% 0.97/1.19 (b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))) <=> b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.97/1.19 inference(symmetry,[status(thm)],[4759])).
% 0.97/1.19 tff(4761,plain,
% 0.97/1.19 ((~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) <=> (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[4760])).
% 0.97/1.19 tff(4762,plain,
% 0.97/1.19 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2425, 206, 4756, 4730])).
% 0.97/1.19 tff(4763,plain,
% 0.97/1.19 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4762, 4761])).
% 0.97/1.19 tff(4764,plain,
% 0.97/1.19 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2431, 4763, 2337])).
% 0.97/1.19 tff(4765,plain,
% 0.97/1.19 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4764, 2474])).
% 0.97/1.19 tff(4766,plain,
% 0.97/1.19 (r(s(s(z)), s(s(s(s(z)))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4562, 1113])).
% 0.97/1.19 tff(4767,plain,
% 0.97/1.19 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[3003, 206, 4756, 1694])).
% 0.97/1.19 tff(4768,plain,
% 0.97/1.19 (r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2688, 150, 2649, 4767])).
% 0.97/1.19 tff(4769,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4770,plain,
% 0.97/1.19 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z))))) <=> ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4771,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[4770])).
% 0.97/1.19 tff(4772,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 0.97/1.19 inference(transitivity,[status(thm)],[4771, 4769])).
% 0.97/1.19 tff(4773,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(4774,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), s(s(z)))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4773, 4772])).
% 0.97/1.19 tff(4775,plain,
% 0.97/1.19 ($false),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4774, 180, 4768, 4766, 4765, 4758])).
% 0.97/1.19 tff(4776,plain,((~b(s(s(elem!1)), z)) | (~(elem!1 = s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~b(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (s(s(elem!1)) = s(elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.19 tff(4777,plain,
% 0.97/1.19 (~b(s(s(elem!1)), z)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4776, 4643, 4705, 4696, 4692, 4688, 4684, 4660, 57, 4663])).
% 0.97/1.19 tff(4778,plain,
% 0.97/1.19 (r(s(s(elem!1)), z)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[228, 4777])).
% 0.97/1.19 tff(4779,plain,
% 0.97/1.19 (r(s(s(s(z))), z)),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4778, 4661])).
% 0.97/1.19 tff(4780,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4781,plain,
% 0.97/1.19 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4782,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[4781])).
% 0.97/1.19 tff(4783,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.97/1.19 inference(transitivity,[status(thm)],[4782, 4780])).
% 0.97/1.19 tff(4784,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(4785,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4784, 4783])).
% 0.97/1.19 tff(4786,plain,
% 0.97/1.19 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4785, 180, 4779, 4660, 4654])).
% 0.97/1.19 tff(4787,plain,
% 0.97/1.19 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2471, 150, 4786, 4650])).
% 0.97/1.19 tff(4788,plain,
% 0.97/1.19 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4787, 4648])).
% 0.97/1.19 tff(4789,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4790,plain,
% 0.97/1.19 (((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4791,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[4790])).
% 0.97/1.19 tff(4792,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 0.97/1.19 inference(transitivity,[status(thm)],[4791, 4789])).
% 0.97/1.19 tff(4793,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(s(s(elem!1)), elem!1)))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(4794,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4793, 4792])).
% 0.97/1.19 tff(4795,plain,
% 0.97/1.19 (~r(s(s(elem!1)), elem!1)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4794, 180, 374, 241])).
% 0.97/1.19 tff(4796,plain,
% 0.97/1.19 (b(s(s(elem!1)), elem!1)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[267, 150, 4795, 4543])).
% 0.97/1.19 tff(4797,plain,
% 0.97/1.19 (~r(elem!1, s(s(s(elem!1))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4526, 180, 374, 60])).
% 0.97/1.19 tff(4798,plain,
% 0.97/1.19 (b(elem!1, s(s(s(elem!1))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[533, 4797, 508])).
% 0.97/1.19 tff(4799,plain,
% 0.97/1.19 ($false),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4559, 206, 4798, 4796, 751])).
% 0.97/1.19 tff(4800,plain,((~r(elem!1, z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = elem!1) | (elem!1 = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.19 tff(4801,plain,
% 0.97/1.19 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4800, 4778, 30, 419, 60, 4672])).
% 0.97/1.19 tff(4802,plain,
% 0.97/1.19 ($false),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4801, 4788])).
% 0.97/1.19 tff(4803,plain,((~r(s(s(s(elem!1))), z)) | (s(s(s(elem!1))) = elem!1) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.19 tff(4804,plain,
% 0.97/1.19 (~r(s(s(s(elem!1))), z)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4803, 59, 58, 11])).
% 0.97/1.19 tff(4805,plain,
% 0.97/1.19 (b(s(s(s(elem!1))), z)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[372, 4804])).
% 0.97/1.19 tff(4806,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4807,plain,
% 0.97/1.19 (((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4808,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[4807])).
% 0.97/1.19 tff(4809,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.19 inference(transitivity,[status(thm)],[4808, 4806])).
% 0.97/1.19 tff(4810,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.19 tff(4811,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), z)) | (~b(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.97/1.19 inference(modus_ponens,[status(thm)],[4810, 4809])).
% 0.97/1.19 tff(4812,plain,
% 0.97/1.19 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4811, 206, 4805, 196])).
% 0.97/1.19 tff(4813,plain,
% 0.97/1.19 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[577, 150, 4812, 83])).
% 0.97/1.19 tff(4814,plain,
% 0.97/1.19 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2818, 206, 4805, 196])).
% 0.97/1.19 tff(4815,plain,
% 0.97/1.19 (r(s(s(s(elem!1))), s(s(elem!1)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[331, 150, 77, 4814])).
% 0.97/1.19 tff(4816,plain,
% 0.97/1.19 (~b(s(s(elem!1)), s(z))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[2363, 196, 911])).
% 0.97/1.19 tff(4817,plain,
% 0.97/1.19 (r(s(s(elem!1)), s(z))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[778, 4816])).
% 0.97/1.19 tff(4818,plain,
% 0.97/1.19 (r(s(s(s(elem!1))), elem!1)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[320, 3635, 58])).
% 0.97/1.19 tff(4819,plain,
% 0.97/1.19 (~r(elem!1, s(s(elem!1)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[673, 4818, 643])).
% 0.97/1.19 tff(4820,plain,
% 0.97/1.19 (b(elem!1, s(s(elem!1)))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[889, 4819, 24])).
% 0.97/1.19 tff(4821,plain,
% 0.97/1.19 (b(elem!1, s(z))),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[3732, 3635, 58, 135, 11])).
% 0.97/1.19 tff(4822,plain,
% 0.97/1.19 (~b(elem!1, z)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[4505, 4821, 911])).
% 0.97/1.19 tff(4823,plain,
% 0.97/1.19 (r(elem!1, z)),
% 0.97/1.19 inference(unit_resolution,[status(thm)],[387, 4822, 135])).
% 0.97/1.19 tff(4824,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4825,plain,
% 0.97/1.19 (((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 0.97/1.19 inference(rewrite,[status(thm)],[])).
% 0.97/1.19 tff(4826,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))))),
% 0.97/1.19 inference(monotonicity,[status(thm)],[4825])).
% 0.97/1.19 tff(4827,plain,
% 0.97/1.19 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1))))),
% 0.97/1.19 inference(transitivity,[status(thm)],[4826, 4824])).
% 0.97/1.19 tff(4828,plain,
% 0.97/1.19 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(elem!1, s(elem!1))))),
% 0.97/1.19 inference(quant_inst,[status(thm)],[])).
% 0.97/1.20 tff(4829,plain,
% 0.97/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(elem!1, s(elem!1)))),
% 0.97/1.20 inference(modus_ponens,[status(thm)],[4828, 4827])).
% 0.97/1.20 tff(4830,plain,
% 0.97/1.20 (~r(elem!1, s(elem!1))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[4829, 180, 270, 4823])).
% 0.97/1.20 tff(4831,plain,
% 0.97/1.20 (b(elem!1, s(elem!1))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[401, 4830, 46])).
% 0.97/1.20 tff(4832,plain,
% 0.97/1.20 ($false),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[4639, 206, 4831, 195, 4820])).
% 0.97/1.20 tff(4833,plain,(b(s(s(s(elem!1))), elem!1) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (elem!1 = z) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.97/1.20 tff(4834,plain,
% 0.97/1.20 (b(s(s(s(elem!1))), elem!1)),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[4833, 195, 270, 2794, 911, 643, 58, 11])).
% 0.97/1.20 tff(4835,plain,
% 0.97/1.20 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[4540, 4834, 4472])).
% 0.97/1.20 tff(4836,plain,
% 0.97/1.20 (r(s(elem!1), s(s(s(elem!1))))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[354, 4835, 18])).
% 0.97/1.20 tff(4837,plain,
% 0.97/1.20 (~b(elem!1, z)),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[662, 4834, 4805])).
% 0.97/1.20 tff(4838,plain,
% 0.97/1.20 (r(elem!1, z)),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[387, 4837, 2794])).
% 0.97/1.20 tff(4839,plain,
% 0.97/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 0.97/1.20 inference(rewrite,[status(thm)],[])).
% 0.97/1.20 tff(4840,plain,
% 0.97/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1))))),
% 0.97/1.20 inference(quant_inst,[status(thm)],[])).
% 0.97/1.20 tff(4841,plain,
% 0.97/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(elem!1, z)) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(elem!1, s(elem!1)))),
% 0.97/1.20 inference(modus_ponens,[status(thm)],[4840, 4839])).
% 0.97/1.20 tff(4842,plain,
% 0.97/1.20 (~r(elem!1, s(elem!1))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[4841, 180, 270, 4838, 4836])).
% 0.97/1.20 tff(4843,plain,
% 0.97/1.20 (b(elem!1, s(elem!1))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[401, 4842, 46])).
% 0.97/1.20 tff(4844,plain,
% 0.97/1.20 (~b(elem!1, s(s(elem!1)))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[4639, 206, 4843, 195])).
% 0.97/1.20 tff(4845,plain,
% 0.97/1.20 (r(elem!1, s(s(elem!1)))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[889, 4844, 24])).
% 0.97/1.20 tff(4846,plain,
% 0.97/1.20 (~b(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[4480, 4834, 4472])).
% 0.97/1.20 tff(4847,plain,
% 0.97/1.20 (r(s(s(s(elem!1))), s(elem!1))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[293, 4846, 11])).
% 0.97/1.20 tff(4848,plain,
% 0.97/1.20 (~r(s(s(s(elem!1))), z)),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[1176, 270, 304])).
% 0.97/1.20 tff(4849,plain,
% 0.97/1.20 (b(s(s(s(elem!1))), z)),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[372, 4848])).
% 0.97/1.20 tff(4850,plain,
% 0.97/1.20 (~b(s(s(s(elem!1))), s(z))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[4020, 4849, 135, 65, 654])).
% 0.97/1.20 tff(4851,plain,
% 0.97/1.20 (r(s(s(s(elem!1))), s(z))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[733, 4850])).
% 0.97/1.20 tff(4852,plain,
% 0.97/1.20 (~r(s(z), s(elem!1))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[436, 4851, 304])).
% 0.97/1.20 tff(4853,plain,
% 0.97/1.20 (b(s(z), s(elem!1))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[467, 4852, 59])).
% 0.97/1.20 tff(4854,plain,
% 0.97/1.20 (~b(elem!1, z)),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[662, 4849, 654])).
% 0.97/1.20 tff(4855,plain,
% 0.97/1.20 (r(elem!1, z)),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[387, 4854, 135])).
% 0.97/1.20 tff(4856,plain,
% 0.97/1.20 (~r(elem!1, s(elem!1))),
% 0.97/1.20 inference(unit_resolution,[status(thm)],[4829, 180, 270, 4855])).
% 1.04/1.20 tff(4857,plain,
% 1.04/1.20 (b(elem!1, s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[401, 4856, 54])).
% 1.04/1.20 tff(4858,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4859,plain,
% 1.04/1.20 (((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4860,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1)))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4859])).
% 1.04/1.20 tff(4861,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[4860, 4858])).
% 1.04/1.20 tff(4862,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(z))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(4863,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4862, 4861])).
% 1.04/1.20 tff(4864,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4863, 206, 4857, 157, 4853])).
% 1.04/1.20 tff(4865,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(z))) | (elem!1 = s(elem!1)) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (elem!1 = z) | (~b(s(s(s(elem!1))), elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4866,plain,
% 1.04/1.20 (~b(elem!1, s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4865, 4847, 59, 270, 46, 4834, 2794, 65])).
% 1.04/1.20 tff(4867,plain,
% 1.04/1.20 (r(elem!1, s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[154, 4866, 65])).
% 1.04/1.20 tff(4868,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4869,plain,
% 1.04/1.20 (((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4870,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1))))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4869])).
% 1.04/1.20 tff(4871,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[4870, 4868])).
% 1.04/1.20 tff(4872,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1)))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(4873,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(elem!1, s(s(elem!1))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4872, 4871])).
% 1.04/1.20 tff(4874,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4873, 180, 4867, 781, 4845])).
% 1.04/1.20 tff(4875,plain,((~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), z)) | (elem!1 = s(z)) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (~b(z, s(z))) | (~r(s(s(s(elem!1))), s(s(elem!1)))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4876,plain,
% 1.04/1.20 (~b(s(s(elem!1)), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4875, 4817, 270, 65, 59, 11, 911, 4815, 58])).
% 1.04/1.20 tff(4877,plain,
% 1.04/1.20 (r(s(s(elem!1)), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[605, 4876, 57])).
% 1.04/1.20 tff(4878,plain,
% 1.04/1.20 (~r(s(z), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[858, 4877, 4817])).
% 1.04/1.20 tff(4879,plain,
% 1.04/1.20 (b(s(z), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[467, 4878, 59])).
% 1.04/1.20 tff(4880,plain,
% 1.04/1.20 (~b(elem!1, z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4505, 157, 911])).
% 1.04/1.20 tff(4881,plain,
% 1.04/1.20 (r(elem!1, z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[387, 4880, 135])).
% 1.04/1.20 tff(4882,plain,
% 1.04/1.20 (~r(elem!1, s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4829, 180, 270, 4881])).
% 1.04/1.20 tff(4883,plain,
% 1.04/1.20 (b(elem!1, s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[401, 4882, 54])).
% 1.04/1.20 tff(4884,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4863, 206, 4883, 157, 607])).
% 1.04/1.20 tff(4885,plain,((~b(elem!1, s(z))) | (~b(s(z), s(elem!1))) | (elem!1 = s(elem!1)) | (~r(s(elem!1), z)) | (elem!1 = z) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4886,plain,
% 1.04/1.20 (~b(elem!1, s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4885, 4879, 46, 270, 2794, 911])).
% 1.04/1.20 tff(4887,plain,
% 1.04/1.20 (b(s(s(s(elem!1))), elem!1)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[3732, 4886, 58, 2794, 11])).
% 1.04/1.20 tff(4888,plain,
% 1.04/1.20 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4480, 4887, 4472])).
% 1.04/1.20 tff(4889,plain,
% 1.04/1.20 (r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[293, 4888, 11])).
% 1.04/1.20 tff(4890,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4891,plain,
% 1.04/1.20 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4892,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4891])).
% 1.04/1.20 tff(4893,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[4892, 4890])).
% 1.04/1.20 tff(4894,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(4895,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4894, 4893])).
% 1.04/1.20 tff(4896,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4895, 180, 4889, 4877, 4813])).
% 1.04/1.20 tff(4897,plain,((~b(s(s(elem!1)), z)) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = elem!1) | (~r(s(elem!1), z)) | (~b(z, s(z))) | (s(z) = s(elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4898,plain,
% 1.04/1.20 (~b(s(s(elem!1)), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4897, 911, 58, 270, 11, 59, 65])).
% 1.04/1.20 tff(4899,plain,
% 1.04/1.20 (r(s(s(elem!1)), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[228, 4898])).
% 1.04/1.20 tff(4900,plain,
% 1.04/1.20 (~r(s(s(elem!1)), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[278, 4899, 270])).
% 1.04/1.20 tff(4901,plain,
% 1.04/1.20 (b(s(s(elem!1)), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[605, 4900, 57])).
% 1.04/1.20 tff(4902,plain,
% 1.04/1.20 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4833, 3635, 270, 2794, 911, 195, 58, 11])).
% 1.04/1.20 tff(4903,plain,
% 1.04/1.20 (b(elem!1, s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[3732, 3635, 58, 2794, 11])).
% 1.04/1.20 tff(4904,plain,
% 1.04/1.20 (~b(s(z), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4885, 4903, 46, 270, 2794, 911])).
% 1.04/1.20 tff(4905,plain,
% 1.04/1.20 (r(s(z), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[467, 4904, 59])).
% 1.04/1.20 tff(4906,plain,
% 1.04/1.20 (~r(s(s(s(elem!1))), s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[436, 158, 304])).
% 1.04/1.20 tff(4907,plain,
% 1.04/1.20 (b(s(s(s(elem!1))), s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[733, 4906])).
% 1.04/1.20 tff(4908,plain,
% 1.04/1.20 (~b(s(z), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[828, 4907, 357])).
% 1.04/1.20 tff(4909,plain,
% 1.04/1.20 (r(s(z), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[794, 4908])).
% 1.04/1.20 tff(4910,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[3718, 180, 270, 4909, 158])).
% 1.04/1.20 tff(4911,plain,((~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4912,plain,
% 1.04/1.20 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4911, 4905, 270, 4805])).
% 1.04/1.20 tff(4913,plain,
% 1.04/1.20 (b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[293, 4912, 11])).
% 1.04/1.20 tff(4914,plain,
% 1.04/1.20 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[640, 4913, 195])).
% 1.04/1.20 tff(4915,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[331, 150, 77, 4914, 4902])).
% 1.04/1.20 tff(4916,plain,(b(s(s(s(elem!1))), elem!1) | (~b(s(s(elem!1)), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(elem!1), z)) | (s(z) = s(elem!1)) | (~b(z, s(z))) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4917,plain,
% 1.04/1.20 (b(s(s(s(elem!1))), elem!1)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4916, 4901, 11, 270, 59, 911, 58])).
% 1.04/1.20 tff(4918,plain,
% 1.04/1.20 (~b(elem!1, z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[662, 4917, 4805])).
% 1.04/1.20 tff(4919,plain,
% 1.04/1.20 (r(elem!1, z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[387, 4918, 2794])).
% 1.04/1.20 tff(4920,plain,
% 1.04/1.20 (~r(elem!1, s(s(elem!1)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4612, 180, 4919, 4899])).
% 1.04/1.20 tff(4921,plain,
% 1.04/1.20 (b(elem!1, s(s(elem!1)))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[889, 4920, 24])).
% 1.04/1.20 tff(4922,plain,
% 1.04/1.20 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4540, 4917, 4472])).
% 1.04/1.20 tff(4923,plain,
% 1.04/1.20 (r(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[354, 4922, 18])).
% 1.04/1.20 tff(4924,plain,
% 1.04/1.20 (~r(elem!1, s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4841, 180, 270, 4919, 4923])).
% 1.04/1.20 tff(4925,plain,
% 1.04/1.20 (b(elem!1, s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[401, 4924, 46])).
% 1.04/1.20 tff(4926,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4639, 206, 4925, 4901, 4921])).
% 1.04/1.20 tff(4927,plain,((~b(z, s(z))) | (~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1)) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = elem!1) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4928,plain,
% 1.04/1.20 (~b(z, s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4927, 270, 11, 59, 58, 65])).
% 1.04/1.20 tff(4929,plain,
% 1.04/1.20 (r(z, s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[505, 4928])).
% 1.04/1.20 tff(4930,plain,
% 1.04/1.20 (~r(s(elem!1), s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[3782, 4929, 270])).
% 1.04/1.20 tff(4931,plain,
% 1.04/1.20 (b(s(elem!1), s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[1652, 4930, 90])).
% 1.04/1.20 tff(4932,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4933,plain,
% 1.04/1.20 (((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4934,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z)))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4933])).
% 1.04/1.20 tff(4935,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[4934, 4932])).
% 1.04/1.20 tff(4936,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(4937,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4936, 4935])).
% 1.04/1.20 tff(4938,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4937, 206, 1168, 157, 3900])).
% 1.04/1.20 tff(4939,plain,((~b(elem!1, s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4940,plain,
% 1.04/1.20 (~b(elem!1, s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4939, 4931, 4472])).
% 1.04/1.20 tff(4941,plain,
% 1.04/1.20 (r(elem!1, s(z))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[154, 4940, 65])).
% 1.04/1.20 tff(4942,plain,
% 1.04/1.20 (b(s(s(s(elem!1))), elem!1)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[3732, 4940, 58, 2794, 11])).
% 1.04/1.20 tff(4943,plain,
% 1.04/1.20 (~b(elem!1, z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[662, 4942, 4805])).
% 1.04/1.20 tff(4944,plain,
% 1.04/1.20 (r(elem!1, z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[387, 4943, 2794])).
% 1.04/1.20 tff(4945,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[3945, 180, 4944, 4941, 4929])).
% 1.04/1.20 tff(4946,plain,((~r(s(elem!1), z)) | (elem!1 = s(z)) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1)) | (s(z) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4947,plain,
% 1.04/1.20 (~r(s(elem!1), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4946, 65, 58, 11, 59])).
% 1.04/1.20 tff(4948,plain,
% 1.04/1.20 (b(s(elem!1), z)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[283, 4947])).
% 1.04/1.20 tff(4949,plain,
% 1.04/1.20 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[723, 206, 4805, 4948])).
% 1.04/1.20 tff(4950,plain,
% 1.04/1.20 (r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[293, 4949, 11])).
% 1.04/1.20 tff(4951,plain,
% 1.04/1.20 (elem!1 = s(z)),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[2368, 96])).
% 1.04/1.20 tff(4952,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[65, 4951])).
% 1.04/1.20 tff(4953,plain,((~(s(z) = elem!1)) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4954,plain,
% 1.04/1.20 (~(s(z) = elem!1)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4953, 65])).
% 1.04/1.20 tff(4955,plain,
% 1.04/1.20 (~b(z, elem!1)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[1188, 95, 4472])).
% 1.04/1.20 tff(4956,plain,
% 1.04/1.20 (r(z, elem!1)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[556, 4955, 910])).
% 1.04/1.20 tff(4957,plain,
% 1.04/1.20 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[723, 206, 4805, 95])).
% 1.04/1.20 tff(4958,plain,
% 1.04/1.20 (r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[293, 4957, 11])).
% 1.04/1.20 tff(4959,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4960,plain,
% 1.04/1.20 (((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4961,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4960])).
% 1.04/1.20 tff(4962,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.04/1.20 inference(transitivity,[status(thm)],[4961, 4959])).
% 1.04/1.20 tff(4963,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(4964,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4963, 4962])).
% 1.04/1.20 tff(4965,plain,
% 1.04/1.20 ($false),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4964, 180, 442, 302, 304])).
% 1.04/1.20 tff(4966,plain,((~r(elem!1, s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.20 tff(4967,plain,
% 1.04/1.20 (~r(elem!1, s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4966, 4818, 4958])).
% 1.04/1.20 tff(4968,plain,
% 1.04/1.20 (b(elem!1, s(elem!1))),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[401, 4967, 46])).
% 1.04/1.20 tff(4969,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4970,plain,
% 1.04/1.20 (((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4971,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1)))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4970])).
% 1.04/1.20 tff(4972,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))))),
% 1.04/1.20 inference(transitivity,[status(thm)],[4971, 4969])).
% 1.04/1.20 tff(4973,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.04/1.20 inference(quant_inst,[status(thm)],[])).
% 1.04/1.20 tff(4974,plain,
% 1.04/1.20 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(s(z), s(elem!1)))),
% 1.04/1.20 inference(modus_ponens,[status(thm)],[4973, 4972])).
% 1.04/1.20 tff(4975,plain,
% 1.04/1.20 (~b(s(z), elem!1)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[4974, 206, 335, 607])).
% 1.04/1.20 tff(4976,plain,
% 1.04/1.20 (r(s(z), elem!1)),
% 1.04/1.20 inference(unit_resolution,[status(thm)],[193, 4975, 156])).
% 1.04/1.20 tff(4977,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4978,plain,
% 1.04/1.20 (((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z))) <=> ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.04/1.20 inference(rewrite,[status(thm)],[])).
% 1.04/1.20 tff(4979,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))))),
% 1.04/1.20 inference(monotonicity,[status(thm)],[4978])).
% 1.04/1.20 tff(4980,plain,
% 1.04/1.20 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 1.04/1.21 inference(transitivity,[status(thm)],[4979, 4977])).
% 1.04/1.21 tff(4981,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), z)))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(4982,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), z)) | (~r(s(z), elem!1))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[4981, 4980])).
% 1.04/1.21 tff(4983,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4982, 180, 169, 543, 780])).
% 1.04/1.21 tff(4984,plain,((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(4985,plain,
% 1.04/1.21 (~r(s(z), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4984, 4976, 543])).
% 1.04/1.21 tff(4986,plain,
% 1.04/1.21 (b(s(z), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[794, 4985])).
% 1.04/1.21 tff(4987,plain,
% 1.04/1.21 (~r(s(z), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4982, 180, 169, 543])).
% 1.04/1.21 tff(4988,plain,
% 1.04/1.21 (b(s(z), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[793, 150, 499, 4987])).
% 1.04/1.21 tff(4989,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4990,plain,
% 1.04/1.21 (((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1)))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(4991,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[4990])).
% 1.04/1.21 tff(4992,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1)))),
% 1.04/1.21 inference(transitivity,[status(thm)],[4991, 4989])).
% 1.04/1.21 tff(4993,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), s(z))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(4994,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(z), elem!1))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[4993, 4992])).
% 1.04/1.21 tff(4995,plain,
% 1.04/1.21 (~r(s(elem!1), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4994, 180, 170, 169])).
% 1.04/1.21 tff(4996,plain,
% 1.04/1.21 (b(s(elem!1), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1651, 150, 99, 4995])).
% 1.04/1.21 tff(4997,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4000, 206, 95, 4996, 4988])).
% 1.04/1.21 tff(4998,plain,((~r(s(z), elem!1)) | (~b(s(elem!1), z)) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(4999,plain,
% 1.04/1.21 (~r(s(elem!1), elem!1)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4998, 4976, 99, 95, 543])).
% 1.04/1.21 tff(5000,plain,
% 1.04/1.21 (b(s(elem!1), elem!1)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[167, 4999, 43])).
% 1.04/1.21 tff(5001,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4623, 206, 5000, 95, 4986, 607])).
% 1.04/1.21 tff(5002,plain,((~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (s(elem!1) = elem!1) | (~r(z, elem!1)) | (s(elem!1) = s(z)) | (s(z) = elem!1) | (~b(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(5003,plain,
% 1.04/1.21 (~b(s(z), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[5002, 4968, 38, 95, 90, 4956, 156])).
% 1.04/1.21 tff(5004,plain,
% 1.04/1.21 (r(s(z), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[467, 5003, 59])).
% 1.04/1.21 tff(5005,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(5006,plain,
% 1.04/1.21 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(5007,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5006])).
% 1.04/1.21 tff(5008,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[5007, 5005])).
% 1.04/1.21 tff(5009,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(5010,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5009, 5008])).
% 1.04/1.21 tff(5011,plain,
% 1.04/1.21 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[5010, 180, 302, 304, 254])).
% 1.04/1.21 tff(5012,plain,
% 1.04/1.21 (~r(s(s(elem!1)), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[858, 158, 254])).
% 1.04/1.21 tff(5013,plain,
% 1.04/1.21 (b(s(s(elem!1)), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[778, 5012])).
% 1.04/1.21 tff(5014,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[759, 5013, 4907, 751])).
% 1.04/1.21 tff(5015,plain,((~r(s(z), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(5016,plain,
% 1.04/1.21 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[5015, 254, 158, 304])).
% 1.04/1.21 tff(5017,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[577, 150, 5016, 5011, 3679])).
% 1.04/1.21 tff(5018,plain,((~r(s(s(elem!1)), s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(5019,plain,
% 1.04/1.21 (~r(s(s(elem!1)), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[5018, 4818, 83, 4958, 5004])).
% 1.04/1.21 tff(5020,plain,
% 1.04/1.21 (b(s(s(elem!1)), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[605, 5019, 57])).
% 1.04/1.21 tff(5021,plain,
% 1.04/1.21 (~r(s(s(s(elem!1))), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[436, 5004, 4958])).
% 1.04/1.21 tff(5022,plain,
% 1.04/1.21 (b(s(s(s(elem!1))), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[733, 5021])).
% 1.04/1.21 tff(5023,plain,
% 1.04/1.21 (~b(s(z), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[832, 5022, 58, 4956, 4903])).
% 1.04/1.21 tff(5024,plain,
% 1.04/1.21 (r(s(z), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[794, 5023])).
% 1.04/1.21 tff(5025,plain,
% 1.04/1.21 (~b(s(s(elem!1)), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[214, 5020, 95])).
% 1.04/1.21 tff(5026,plain,
% 1.04/1.21 (r(s(s(elem!1)), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[228, 5025])).
% 1.04/1.21 tff(5027,plain,
% 1.04/1.21 (~r(s(s(elem!1)), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[789, 5026, 5024])).
% 1.04/1.21 tff(5028,plain,
% 1.04/1.21 (b(s(s(elem!1)), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[778, 5027])).
% 1.04/1.21 tff(5029,plain,
% 1.04/1.21 (~b(elem!1, s(s(elem!1)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[703, 5028, 5020, 4903])).
% 1.04/1.21 tff(5030,plain,
% 1.04/1.21 (r(elem!1, s(s(elem!1)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[889, 5029, 24])).
% 1.04/1.21 tff(5031,plain,
% 1.04/1.21 (~b(elem!1, z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4492, 95, 4472])).
% 1.04/1.21 tff(5032,plain,
% 1.04/1.21 (r(elem!1, z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[387, 5031, 2794])).
% 1.04/1.21 tff(5033,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4612, 180, 5032, 5026, 5030])).
% 1.04/1.21 tff(5034,plain,(b(s(s(s(elem!1))), elem!1) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = elem!1) | (s(z) = s(elem!1)) | (s(z) = elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(5035,plain,
% 1.04/1.21 (b(s(s(s(elem!1))), elem!1)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[5034, 4948, 58, 59, 4954, 11])).
% 1.04/1.21 tff(5036,plain,
% 1.04/1.21 (~b(s(s(s(elem!1))), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4020, 5035, 2794, 4805, 65])).
% 1.04/1.21 tff(5037,plain,
% 1.04/1.21 (r(s(s(s(elem!1))), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[733, 5036])).
% 1.04/1.21 tff(5038,plain,
% 1.04/1.21 (~r(s(z), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[436, 5037, 4950])).
% 1.04/1.21 tff(5039,plain,
% 1.04/1.21 (b(s(z), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[467, 5038, 59])).
% 1.04/1.21 tff(5040,plain,
% 1.04/1.21 (~b(z, elem!1)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1188, 4948, 4472])).
% 1.04/1.21 tff(5041,plain,
% 1.04/1.21 (r(z, elem!1)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[556, 5040, 910])).
% 1.04/1.21 tff(5042,plain,
% 1.04/1.21 (~b(elem!1, s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[5002, 5039, 38, 4948, 90, 5041, 4954])).
% 1.04/1.21 tff(5043,plain,
% 1.04/1.21 (r(elem!1, s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[401, 5042, 46])).
% 1.04/1.21 tff(5044,plain,
% 1.04/1.21 (~r(z, s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[939, 5043, 5041])).
% 1.04/1.21 tff(5045,plain,
% 1.04/1.21 (b(z, s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[817, 150, 5044, 235])).
% 1.04/1.21 tff(5046,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(5047,plain,
% 1.04/1.21 (((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z))) <=> ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(5048,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5047])).
% 1.04/1.21 tff(5049,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[5048, 5046])).
% 1.04/1.21 tff(5050,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(z), z)))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(5051,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(z), z)) | (~b(s(z), s(elem!1)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5050, 5049])).
% 1.04/1.21 tff(5052,plain,
% 1.04/1.21 (~b(s(z), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[5051, 206, 5039, 5045])).
% 1.04/1.21 tff(5053,plain,
% 1.04/1.21 (r(s(z), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[794, 5052])).
% 1.04/1.21 tff(5054,plain,
% 1.04/1.21 (~r(s(z), elem!1)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4984, 5053, 5041])).
% 1.04/1.21 tff(5055,plain,
% 1.04/1.21 (b(s(z), elem!1)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[193, 5054, 4954])).
% 1.04/1.21 tff(5056,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(5057,plain,
% 1.04/1.21 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(5058,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5057])).
% 1.04/1.21 tff(5059,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[5058, 5056])).
% 1.04/1.21 tff(5060,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(5061,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(z), s(elem!1)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5060, 5059])).
% 1.04/1.21 tff(5062,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[5061, 206, 4472, 5055, 5039])).
% 1.04/1.21 tff(5063,plain,((elem!1 = s(z)) | (s(z) = s(elem!1)) | (s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(5064,plain,
% 1.04/1.21 (elem!1 = s(z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[5063, 59, 58, 11])).
% 1.04/1.21 tff(5065,plain,
% 1.04/1.21 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(elem!1))), s(z))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5064])).
% 1.04/1.21 tff(5066,plain,
% 1.04/1.21 (~r(s(s(s(elem!1))), elem!1)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2322, 5064, 2794, 58, 11])).
% 1.04/1.21 tff(5067,plain,
% 1.04/1.21 (b(s(s(s(elem!1))), elem!1)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[320, 5066, 58])).
% 1.04/1.21 tff(5068,plain,
% 1.04/1.21 (b(s(s(s(elem!1))), s(z))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5067, 5065])).
% 1.04/1.21 tff(5069,plain,
% 1.04/1.21 (~b(z, s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[3137, 5068, 4805])).
% 1.04/1.21 tff(5070,plain,
% 1.04/1.21 (r(z, s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[505, 5069])).
% 1.04/1.21 tff(5071,plain,
% 1.04/1.21 (s(elem!1) = s(s(z))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5064])).
% 1.04/1.21 tff(5072,plain,
% 1.04/1.21 (b(s(elem!1), s(z)) <=> b(s(s(z)), s(z))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5071])).
% 1.04/1.21 tff(5073,plain,
% 1.04/1.21 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5064])).
% 1.04/1.21 tff(5074,plain,
% 1.04/1.21 (b(s(elem!1), s(z))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[4472, 5073])).
% 1.04/1.21 tff(5075,plain,
% 1.04/1.21 (b(s(s(z)), s(z))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5074, 5072])).
% 1.04/1.21 tff(5076,plain,
% 1.04/1.21 (s(s(elem!1)) = s(s(s(z)))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5071])).
% 1.04/1.21 tff(5077,plain,
% 1.04/1.21 (s(s(s(elem!1))) = s(s(s(s(z))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5076])).
% 1.04/1.21 tff(5078,plain,
% 1.04/1.21 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(z)))), s(z))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5077])).
% 1.04/1.21 tff(5079,plain,
% 1.04/1.21 (b(s(s(s(s(z)))), s(z))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5068, 5078])).
% 1.04/1.21 tff(5080,plain,
% 1.04/1.21 (b(s(s(s(elem!1))), z) <=> b(s(s(s(s(z)))), z)),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5077])).
% 1.04/1.21 tff(5081,plain,
% 1.04/1.21 (b(s(s(s(s(z)))), z)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[4805, 5080])).
% 1.04/1.21 tff(5082,plain,
% 1.04/1.21 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.04/1.21 inference(symmetry,[status(thm)],[5077])).
% 1.04/1.21 tff(5083,plain,
% 1.04/1.21 (s(s(z)) = s(elem!1)),
% 1.04/1.21 inference(symmetry,[status(thm)],[5071])).
% 1.04/1.21 tff(5084,plain,
% 1.04/1.21 (r(s(s(z)), s(s(s(s(z))))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5083, 5082])).
% 1.04/1.21 tff(5085,plain,
% 1.04/1.21 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.21 inference(symmetry,[status(thm)],[5084])).
% 1.04/1.21 tff(5086,plain,
% 1.04/1.21 (~b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4540, 5067, 4472])).
% 1.04/1.21 tff(5087,plain,
% 1.04/1.21 (r(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[354, 5086, 18])).
% 1.04/1.21 tff(5088,plain,
% 1.04/1.21 (r(s(s(z)), s(s(s(s(z)))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5087, 5085])).
% 1.04/1.21 tff(5089,plain,
% 1.04/1.21 (r(s(s(s(s(s(elem!1))))), s(s(z)))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2653, 150, 2650, 3058])).
% 1.04/1.21 tff(5090,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(5091,plain,
% 1.04/1.21 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(5092,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5091])).
% 1.04/1.21 tff(5093,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[5092, 5090])).
% 1.04/1.21 tff(5094,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(5095,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z))))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5094, 5093])).
% 1.04/1.21 tff(5096,plain,
% 1.04/1.21 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[5095, 206, 3019, 2200, 4730])).
% 1.04/1.21 tff(5097,plain,
% 1.04/1.21 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5096, 4761])).
% 1.04/1.21 tff(5098,plain,
% 1.04/1.21 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2431, 5097, 2337])).
% 1.04/1.21 tff(5099,plain,
% 1.04/1.21 (r(s(s(s(s(s(elem!1))))), s(s(s(s(z)))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5098, 2474])).
% 1.04/1.21 tff(5100,assumption,(r(s(s(z)), s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.21 tff(5101,plain,
% 1.04/1.21 (~b(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[3003, 206, 3019, 1694])).
% 1.04/1.21 tff(5102,plain,
% 1.04/1.21 (r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2688, 150, 2649, 5101])).
% 1.04/1.21 tff(5103,plain,
% 1.04/1.21 ($false),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4774, 180, 5102, 5100, 5099, 5089])).
% 1.04/1.21 tff(5104,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~(elem!1 = s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.21 tff(5105,plain,
% 1.04/1.21 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[5104, 5088, 5064, 5081, 5079, 5075])).
% 1.04/1.21 tff(5106,plain,
% 1.04/1.21 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2578, 5105])).
% 1.04/1.21 tff(5107,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(5108,plain,
% 1.04/1.21 (((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z))) <=> ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.04/1.21 inference(rewrite,[status(thm)],[])).
% 1.04/1.21 tff(5109,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z)))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5108])).
% 1.04/1.21 tff(5110,plain,
% 1.04/1.21 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))))),
% 1.04/1.21 inference(transitivity,[status(thm)],[5109, 5107])).
% 1.04/1.21 tff(5111,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), z)))),
% 1.04/1.21 inference(quant_inst,[status(thm)],[])).
% 1.04/1.21 tff(5112,plain,
% 1.04/1.21 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(z, s(z))) | (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5111, 5110])).
% 1.04/1.21 tff(5113,plain,
% 1.04/1.21 (~r(s(s(s(s(s(elem!1))))), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[5112, 180, 5106, 5070])).
% 1.04/1.21 tff(5114,plain,
% 1.04/1.21 (b(s(s(s(s(s(elem!1))))), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2388, 150, 1395, 5113])).
% 1.04/1.21 tff(5115,plain,
% 1.04/1.21 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5076])).
% 1.04/1.21 tff(5116,plain,
% 1.04/1.21 (r(elem!1, z) <=> r(s(z), z)),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5064])).
% 1.04/1.21 tff(5117,plain,
% 1.04/1.21 (~b(elem!1, z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[662, 5067, 4805])).
% 1.04/1.21 tff(5118,plain,
% 1.04/1.21 (r(elem!1, z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[387, 5117, 2794])).
% 1.04/1.21 tff(5119,plain,
% 1.04/1.21 (r(s(z), z)),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5118, 5116])).
% 1.04/1.21 tff(5120,plain,
% 1.04/1.21 (b(s(s(elem!1)), s(elem!1)) <=> b(s(s(s(z))), s(s(z)))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5076, 5071])).
% 1.04/1.21 tff(5121,plain,
% 1.04/1.21 (b(s(s(s(z))), s(s(z))) <=> b(s(s(elem!1)), s(elem!1))),
% 1.04/1.21 inference(symmetry,[status(thm)],[5120])).
% 1.04/1.21 tff(5122,plain,
% 1.04/1.21 (s(s(s(z))) = s(s(elem!1))),
% 1.04/1.21 inference(symmetry,[status(thm)],[5076])).
% 1.04/1.21 tff(5123,plain,
% 1.04/1.21 ((s(s(s(z))) = s(s(z))) <=> (s(s(elem!1)) = s(elem!1))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5122, 5083])).
% 1.04/1.21 tff(5124,plain,
% 1.04/1.21 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(z))) = s(s(z)))),
% 1.04/1.21 inference(symmetry,[status(thm)],[5123])).
% 1.04/1.21 tff(5125,plain,
% 1.04/1.21 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(s(z))) = s(s(z))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5124])).
% 1.04/1.21 tff(5126,plain,
% 1.04/1.21 (~(s(s(s(z))) = s(s(z)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[57, 5125])).
% 1.04/1.21 tff(5127,plain,
% 1.04/1.21 (r(s(s(s(s(z)))), s(s(z))) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5082])).
% 1.04/1.21 tff(5128,plain,
% 1.04/1.21 (r(s(s(s(elem!1))), s(s(z))) <=> r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.21 inference(symmetry,[status(thm)],[5127])).
% 1.04/1.21 tff(5129,plain,
% 1.04/1.21 (r(s(s(s(elem!1))), s(elem!1)) <=> r(s(s(s(elem!1))), s(s(z)))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[5071])).
% 1.04/1.21 tff(5130,plain,
% 1.04/1.21 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4480, 5067, 4472])).
% 1.04/1.21 tff(5131,plain,
% 1.04/1.21 (r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[293, 5130, 11])).
% 1.04/1.21 tff(5132,plain,
% 1.04/1.21 (r(s(s(s(elem!1))), s(s(z)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5131, 5129])).
% 1.04/1.21 tff(5133,plain,
% 1.04/1.21 (r(s(s(s(s(z)))), s(s(z)))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5132, 5128])).
% 1.04/1.21 tff(5134,plain,
% 1.04/1.21 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[1299, 150, 1296, 1934])).
% 1.04/1.21 tff(5135,plain,
% 1.04/1.21 (b(s(s(elem!1)), z) <=> b(s(s(s(z))), z)),
% 1.04/1.21 inference(monotonicity,[status(thm)],[1002])).
% 1.04/1.21 tff(5136,plain,
% 1.04/1.21 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.21 inference(monotonicity,[status(thm)],[1002, 1003])).
% 1.04/1.21 tff(5137,plain,
% 1.04/1.21 (b(s(s(s(z))), s(s(s(s(z))))) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.21 inference(symmetry,[status(thm)],[5136])).
% 1.04/1.21 tff(5138,plain,
% 1.04/1.21 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[4713, 180, 1313, 1691])).
% 1.04/1.21 tff(5139,plain,
% 1.04/1.21 (b(s(s(s(z))), s(s(s(s(z)))))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[2471, 150, 5138, 2468])).
% 1.04/1.21 tff(5140,plain,
% 1.04/1.21 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.21 inference(modus_ponens,[status(thm)],[5139, 5137])).
% 1.04/1.21 tff(5141,plain,
% 1.04/1.21 (~b(s(s(elem!1)), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[759, 5140, 735])).
% 1.04/1.21 tff(5142,plain,
% 1.04/1.21 (r(s(s(elem!1)), s(z))),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[778, 5141])).
% 1.04/1.21 tff(5143,plain,
% 1.04/1.21 (~r(s(s(elem!1)), z)),
% 1.04/1.21 inference(unit_resolution,[status(thm)],[789, 5142, 780])).
% 1.04/1.22 tff(5144,plain,
% 1.04/1.22 (b(s(s(elem!1)), z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[228, 5143])).
% 1.04/1.22 tff(5145,plain,
% 1.04/1.22 (b(s(s(s(z))), z)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5144, 5135])).
% 1.04/1.22 tff(5146,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5147,plain,
% 1.04/1.22 (((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5148,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[5147])).
% 1.04/1.22 tff(5149,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[5148, 5146])).
% 1.04/1.22 tff(5150,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(5151,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), s(s(s(z)))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5150, 5149])).
% 1.04/1.22 tff(5152,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5151, 206, 2200, 5145, 5134])).
% 1.04/1.22 tff(5153,plain,((~r(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~(elem!1 = s(z))) | (~r(s(z), z)) | (~b(s(s(s(elem!1))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(5154,plain,
% 1.04/1.22 (~r(s(s(s(z))), s(s(z)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5153, 5081, 5064, 5119, 5068, 5133])).
% 1.04/1.22 tff(5155,plain,
% 1.04/1.22 (b(s(s(s(z))), s(s(z)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1307, 5154, 5126])).
% 1.04/1.22 tff(5156,plain,
% 1.04/1.22 (b(s(s(elem!1)), s(elem!1))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5155, 5121])).
% 1.04/1.22 tff(5157,plain,
% 1.04/1.22 (b(s(s(s(z))), s(s(z)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[195, 1896])).
% 1.04/1.22 tff(5158,plain,
% 1.04/1.22 (r(s(s(s(z))), z)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[229, 1895])).
% 1.04/1.22 tff(5159,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5160,plain,
% 1.04/1.22 (((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5161,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[5160])).
% 1.04/1.22 tff(5162,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z)))),
% 1.04/1.22 inference(transitivity,[status(thm)],[5161, 5159])).
% 1.04/1.22 tff(5163,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(5164,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), z))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5163, 5162])).
% 1.04/1.22 tff(5165,plain,
% 1.04/1.22 (~r(s(s(s(z))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5164, 180, 780, 5158])).
% 1.04/1.22 tff(5166,plain,
% 1.04/1.22 (b(s(s(s(z))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1865, 5165, 1721])).
% 1.04/1.22 tff(5167,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1792, 206, 1694, 5166, 5157])).
% 1.04/1.22 tff(5168,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(z)), s(z))) | (~r(s(z), z)) | (~(elem!1 = s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(5169,plain,
% 1.04/1.22 (~b(s(elem!1), z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5168, 5156, 5119, 5064, 5075])).
% 1.04/1.22 tff(5170,plain,
% 1.04/1.22 (r(s(elem!1), z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[283, 5169])).
% 1.04/1.22 tff(5171,plain,
% 1.04/1.22 (~r(s(z), s(elem!1))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[4911, 5170, 5131, 4805])).
% 1.04/1.22 tff(5172,plain,
% 1.04/1.22 (b(s(z), s(elem!1))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[467, 5171, 59])).
% 1.04/1.22 tff(5173,plain,
% 1.04/1.22 (~r(s(s(elem!1)), z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[3724, 5172, 5119, 57, 5170])).
% 1.04/1.22 tff(5174,plain,
% 1.04/1.22 (b(s(s(elem!1)), z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[228, 5173])).
% 1.04/1.22 tff(5175,plain,
% 1.04/1.22 (b(s(s(s(z))), z)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5174, 5115])).
% 1.04/1.22 tff(5176,plain,
% 1.04/1.22 (~(s(s(s(z))) = s(s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2439, 5064])).
% 1.04/1.22 tff(5177,plain,
% 1.04/1.22 (~(s(s(s(z))) = s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1720, 5064])).
% 1.04/1.22 tff(5178,plain,
% 1.04/1.22 (~b(s(s(s(z))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1804, 5170, 5064, 4805, 38, 57, 5068])).
% 1.04/1.22 tff(5179,plain,
% 1.04/1.22 (r(s(s(s(z))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1865, 5178, 5177])).
% 1.04/1.22 tff(5180,plain,
% 1.04/1.22 (~r(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2588, 5106, 5179])).
% 1.04/1.22 tff(5181,plain,
% 1.04/1.22 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2455, 150, 5180, 5176])).
% 1.04/1.22 tff(5182,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[3886, 206, 5181, 5175, 5114])).
% 1.04/1.22 tff(5183,plain,((s(z) = s(elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (s(s(s(elem!1))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(5184,plain,
% 1.04/1.22 (s(z) = s(elem!1)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5183, 58, 11])).
% 1.04/1.22 tff(5185,plain,
% 1.04/1.22 (b(z, s(z)) <=> b(z, s(elem!1))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[5184])).
% 1.04/1.22 tff(5186,plain,
% 1.04/1.22 (b(z, s(elem!1)) <=> b(z, s(z))),
% 1.04/1.22 inference(symmetry,[status(thm)],[5185])).
% 1.04/1.22 tff(5187,plain,
% 1.04/1.22 (s(elem!1) = s(z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[101, 5184])).
% 1.04/1.22 tff(5188,plain,
% 1.04/1.22 (z = elem!1),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[111, 5187])).
% 1.04/1.22 tff(5189,plain,
% 1.04/1.22 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[5188])).
% 1.04/1.22 tff(5190,plain,
% 1.04/1.22 (b(elem!1, s(elem!1)) <=> b(z, s(elem!1))),
% 1.04/1.22 inference(symmetry,[status(thm)],[5189])).
% 1.04/1.22 tff(5191,plain,
% 1.04/1.22 (b(elem!1, s(elem!1)) <=> b(z, s(z))),
% 1.04/1.22 inference(transitivity,[status(thm)],[5190, 5186])).
% 1.04/1.22 tff(5192,plain,
% 1.04/1.22 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 1.04/1.22 inference(monotonicity,[status(thm)],[112])).
% 1.04/1.22 tff(5193,plain,
% 1.04/1.22 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 1.04/1.22 inference(symmetry,[status(thm)],[5192])).
% 1.04/1.22 tff(5194,plain,
% 1.04/1.22 (b(s(elem!1), z)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1168, 5193])).
% 1.04/1.22 tff(5195,plain,
% 1.04/1.22 (b(s(z), elem!1)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1168, 114])).
% 1.04/1.22 tff(5196,plain,
% 1.04/1.22 (b(s(z), z) <=> b(s(elem!1), z)),
% 1.04/1.22 inference(monotonicity,[status(thm)],[97])).
% 1.04/1.22 tff(5197,plain,
% 1.04/1.22 (b(s(elem!1), z) <=> b(s(z), z)),
% 1.04/1.22 inference(symmetry,[status(thm)],[5196])).
% 1.04/1.22 tff(5198,plain,
% 1.04/1.22 (b(s(elem!1), elem!1) <=> b(s(z), z)),
% 1.04/1.22 inference(transitivity,[status(thm)],[5193, 5197])).
% 1.04/1.22 tff(5199,plain,
% 1.04/1.22 (b(s(z), z)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1168, 5198])).
% 1.04/1.22 tff(5200,plain,
% 1.04/1.22 (b(s(s(s(elem!1))), z)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[3185, 654, 112])).
% 1.04/1.22 tff(5201,plain,
% 1.04/1.22 (~b(s(s(s(elem!1))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[828, 5200, 5199])).
% 1.04/1.22 tff(5202,plain,
% 1.04/1.22 (r(s(s(s(elem!1))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[733, 5201])).
% 1.04/1.22 tff(5203,plain,
% 1.04/1.22 (b(s(s(s(z))), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 1.04/1.22 inference(monotonicity,[status(thm)],[2878])).
% 1.04/1.22 tff(5204,plain,
% 1.04/1.22 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(z))), elem!1)),
% 1.04/1.22 inference(symmetry,[status(thm)],[5203])).
% 1.04/1.22 tff(5205,plain,
% 1.04/1.22 (b(s(s(s(z))), elem!1)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[654, 5204])).
% 1.04/1.22 tff(5206,assumption,(s(z) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.04/1.22 tff(5207,plain,
% 1.04/1.22 (s(s(s(s(s(s(elem!1)))))) = s(z)),
% 1.04/1.22 inference(symmetry,[status(thm)],[5206])).
% 1.04/1.22 tff(5208,plain,
% 1.04/1.22 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(z))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[5207])).
% 1.04/1.22 tff(5209,plain,
% 1.04/1.22 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(symmetry,[status(thm)],[5208])).
% 1.04/1.22 tff(5210,plain,
% 1.04/1.22 (elem!1 = z),
% 1.04/1.22 inference(symmetry,[status(thm)],[133])).
% 1.04/1.22 tff(5211,plain,
% 1.04/1.22 (elem!1 = s(s(s(s(s(elem!1)))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[5210, 107, 5209, 1023])).
% 1.04/1.22 tff(5212,plain,
% 1.04/1.22 ((s(s(s(s(s(elem!1))))) = z) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.04/1.22 inference(monotonicity,[status(thm)],[133])).
% 1.04/1.22 tff(5213,plain,
% 1.04/1.22 ((s(s(s(s(s(elem!1))))) = z) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[5212, 63])).
% 1.04/1.22 tff(5214,plain,
% 1.04/1.22 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[5213])).
% 1.04/1.22 tff(5215,plain,
% 1.04/1.22 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1395, 5214])).
% 1.04/1.22 tff(5216,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5215, 5211])).
% 1.04/1.22 tff(5217,plain,((~(s(z) = s(s(s(s(s(s(elem!1)))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(5218,plain,
% 1.04/1.22 (~(s(z) = s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5217, 2926])).
% 1.04/1.22 tff(5219,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5220,plain,
% 1.04/1.22 (((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5221,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[5220])).
% 1.04/1.22 tff(5222,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[5221, 5219])).
% 1.04/1.22 tff(5223,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(5224,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5223, 5222])).
% 1.04/1.22 tff(5225,plain,
% 1.04/1.22 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5224, 206, 117, 3375])).
% 1.04/1.22 tff(5226,plain,
% 1.04/1.22 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1515, 5225, 5218])).
% 1.04/1.22 tff(5227,plain,
% 1.04/1.22 (r(s(s(s(z))), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[2878])).
% 1.04/1.22 tff(5228,plain,
% 1.04/1.22 (r(s(s(s(elem!1))), s(z)) <=> r(s(s(s(z))), s(z))),
% 1.04/1.22 inference(symmetry,[status(thm)],[5227])).
% 1.04/1.22 tff(5229,plain,
% 1.04/1.22 (r(s(s(s(z))), s(z))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[243, 5228])).
% 1.04/1.22 tff(5230,assumption,(r(s(z), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.04/1.22 tff(5231,plain,
% 1.04/1.22 ((~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), s(z)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1889, 180, 5230])).
% 1.04/1.22 tff(5232,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5231, 5229, 3345])).
% 1.04/1.22 tff(5233,plain,((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(elem!1))), s(z))) | (~(s(elem!1) = s(z))) | (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(5234,plain,
% 1.04/1.22 (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5233, 5226, 86, 243])).
% 1.04/1.22 tff(5235,plain,
% 1.04/1.22 (b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1088, 5234, 2993])).
% 1.04/1.22 tff(5236,plain,
% 1.04/1.22 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5235, 3337])).
% 1.04/1.22 tff(5237,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5238,plain,
% 1.04/1.22 (((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5239,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[5238])).
% 1.04/1.22 tff(5240,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[5239, 5237])).
% 1.04/1.22 tff(5241,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(5242,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5241, 5240])).
% 1.04/1.22 tff(5243,plain,
% 1.04/1.22 ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5242, 206, 3375])).
% 1.04/1.22 tff(5244,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5243, 5236, 5205])).
% 1.04/1.22 tff(5245,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~(s(elem!1) = s(z))) | (~b(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(5246,plain,
% 1.04/1.22 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5245, 5202, 102, 5195, 654])).
% 1.04/1.22 tff(5247,plain,
% 1.04/1.22 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[3090, 5246, 4135])).
% 1.04/1.22 tff(5248,plain,
% 1.04/1.22 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[4480, 654, 1168])).
% 1.04/1.22 tff(5249,plain,
% 1.04/1.22 (r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[293, 5248, 11])).
% 1.04/1.22 tff(5250,plain,
% 1.04/1.22 (r(s(s(s(s(s(elem!1))))), s(elem!1)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[4218])).
% 1.04/1.22 tff(5251,plain,
% 1.04/1.22 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.22 inference(symmetry,[status(thm)],[5250])).
% 1.04/1.22 tff(5252,plain,
% 1.04/1.22 (r(s(s(z)), elem!1)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[229, 4068])).
% 1.04/1.22 tff(5253,plain,
% 1.04/1.22 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[97])).
% 1.04/1.22 tff(5254,plain,
% 1.04/1.22 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.04/1.22 inference(symmetry,[status(thm)],[5253])).
% 1.04/1.22 tff(5255,plain,
% 1.04/1.22 (b(z, s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[112])).
% 1.04/1.22 tff(5256,plain,
% 1.04/1.22 (b(z, s(z)) <=> b(z, s(elem!1))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[97])).
% 1.04/1.22 tff(5257,plain,
% 1.04/1.22 (b(z, s(z)) <=> b(elem!1, s(z))),
% 1.04/1.22 inference(transitivity,[status(thm)],[5256, 5255, 5254])).
% 1.04/1.22 tff(5258,plain,
% 1.04/1.22 (r(s(s(elem!1)), elem!1)),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[229, 4067])).
% 1.04/1.22 tff(5259,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5260,plain,
% 1.04/1.22 (((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5261,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[5260])).
% 1.04/1.22 tff(5262,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[5261, 5259])).
% 1.04/1.22 tff(5263,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(5264,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5263, 5262])).
% 1.04/1.22 tff(5265,plain,
% 1.04/1.22 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5264, 180, 4274, 5258])).
% 1.04/1.22 tff(5266,plain,
% 1.04/1.22 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[4409, 150, 4380, 5265])).
% 1.04/1.22 tff(5267,assumption,(b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 1.04/1.22 tff(5268,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5269,plain,
% 1.04/1.22 (((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5270,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[5269])).
% 1.04/1.22 tff(5271,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[5270, 5268])).
% 1.04/1.22 tff(5272,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(5273,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5272, 5271])).
% 1.04/1.22 tff(5274,plain,
% 1.04/1.22 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5273, 206, 195, 5267])).
% 1.04/1.22 tff(5275,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5274, 4221])).
% 1.04/1.22 tff(5276,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~(s(z) = s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(5277,plain,
% 1.04/1.22 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5276, 195, 97, 5266])).
% 1.04/1.22 tff(5278,plain,
% 1.04/1.22 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1402, 5277])).
% 1.04/1.22 tff(5279,plain,
% 1.04/1.22 (~r(z, s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[1611, 5278, 4080, 243, 357])).
% 1.04/1.22 tff(5280,plain,
% 1.04/1.22 (b(z, s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[505, 5279])).
% 1.04/1.22 tff(5281,plain,
% 1.04/1.22 (b(elem!1, s(z))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5280, 5257])).
% 1.04/1.22 tff(5282,plain,
% 1.04/1.22 ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(z)), elem!1)) | (s(s(s(s(s(elem!1))))) = elem!1) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z)))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[3077, 2650])).
% 1.04/1.22 tff(5283,plain,
% 1.04/1.22 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5282, 5281, 4088, 4050, 5252])).
% 1.04/1.22 tff(5284,plain,
% 1.04/1.22 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2578, 5283])).
% 1.04/1.22 tff(5285,plain,
% 1.04/1.22 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5284, 5251])).
% 1.04/1.22 tff(5286,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5287,plain,
% 1.04/1.22 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5288,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[5287])).
% 1.04/1.22 tff(5289,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[5288, 5286])).
% 1.04/1.22 tff(5290,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.22 inference(quant_inst,[status(thm)],[])).
% 1.04/1.22 tff(5291,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[5290, 5289])).
% 1.04/1.22 tff(5292,plain,
% 1.04/1.22 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5291, 180, 304, 5285])).
% 1.04/1.22 tff(5293,plain,
% 1.04/1.22 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[2431, 5292, 4090])).
% 1.04/1.22 tff(5294,plain,
% 1.04/1.22 (r(s(s(s(s(s(s(elem!1)))))), s(z)) <=> r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[97])).
% 1.04/1.22 tff(5295,plain,
% 1.04/1.22 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.04/1.22 inference(modus_ponens,[status(thm)],[1405, 5294])).
% 1.04/1.22 tff(5296,assumption,(~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))), introduced(assumption)).
% 1.04/1.22 tff(5297,plain,
% 1.04/1.22 ($false),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5296, 5295])).
% 1.04/1.22 tff(5298,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(z))) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.22 tff(5299,plain,
% 1.04/1.22 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.04/1.22 inference(unit_resolution,[status(thm)],[5298, 5278, 97])).
% 1.04/1.22 tff(5300,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5301,plain,
% 1.04/1.22 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.04/1.22 inference(rewrite,[status(thm)],[])).
% 1.04/1.22 tff(5302,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 1.04/1.22 inference(monotonicity,[status(thm)],[5301])).
% 1.04/1.22 tff(5303,plain,
% 1.04/1.22 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.04/1.22 inference(transitivity,[status(thm)],[5302, 5300])).
% 1.04/1.22 tff(5304,plain,
% 1.04/1.22 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(5305,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[5304, 5303])).
% 1.04/1.23 tff(5306,plain,
% 1.04/1.23 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5305, 180, 304, 5299])).
% 1.04/1.23 tff(5307,plain,
% 1.04/1.23 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1365, 5306, 4213])).
% 1.04/1.23 tff(5308,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5309,plain,
% 1.04/1.23 (((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5310,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[5309])).
% 1.04/1.23 tff(5311,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[5310, 5308])).
% 1.04/1.23 tff(5312,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(5313,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[5312, 5311])).
% 1.04/1.23 tff(5314,plain,
% 1.04/1.23 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5313, 180, 5299, 5285])).
% 1.04/1.23 tff(5315,plain,
% 1.04/1.23 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[3033, 5314, 4091])).
% 1.04/1.23 tff(5316,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5317,plain,
% 1.04/1.23 (((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5318,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[5317])).
% 1.04/1.23 tff(5319,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[5318, 5316])).
% 1.04/1.23 tff(5320,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(5321,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[5320, 5319])).
% 1.04/1.23 tff(5322,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5321, 206, 5315, 5307, 5293])).
% 1.04/1.23 tff(5323,plain,((~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~(s(z) = s(elem!1))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(elem!1))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(5324,plain,
% 1.04/1.23 (~b(s(s(elem!1)), s(elem!1))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5323, 5249, 97, 5202, 5200, 5247, 5194])).
% 1.04/1.23 tff(5325,plain,
% 1.04/1.23 (r(s(s(elem!1)), s(elem!1))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[605, 5324, 57])).
% 1.04/1.23 tff(5326,plain,
% 1.04/1.23 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[300, 180, 5249, 5325])).
% 1.04/1.23 tff(5327,plain,
% 1.04/1.23 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[331, 150, 77, 5326])).
% 1.04/1.23 tff(5328,plain,
% 1.04/1.23 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[97])).
% 1.04/1.23 tff(5329,plain,
% 1.04/1.23 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 1.04/1.23 inference(symmetry,[status(thm)],[5328])).
% 1.04/1.23 tff(5330,plain,
% 1.04/1.23 (r(s(s(elem!1)), s(z))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[5325, 5329])).
% 1.04/1.23 tff(5331,plain,
% 1.04/1.23 ((s(z) = elem!1) <=> (s(elem!1) = elem!1)),
% 1.04/1.23 inference(monotonicity,[status(thm)],[97])).
% 1.04/1.23 tff(5332,plain,
% 1.04/1.23 ((s(z) = elem!1) <=> (elem!1 = s(elem!1))),
% 1.04/1.23 inference(transitivity,[status(thm)],[5331, 39])).
% 1.04/1.23 tff(5333,plain,
% 1.04/1.23 ((elem!1 = s(elem!1)) <=> (s(z) = elem!1)),
% 1.04/1.23 inference(symmetry,[status(thm)],[5332])).
% 1.04/1.23 tff(5334,plain,
% 1.04/1.23 ((elem!1 = s(elem!1)) <=> (elem!1 = s(z))),
% 1.04/1.23 inference(transitivity,[status(thm)],[5333, 96])).
% 1.04/1.23 tff(5335,plain,
% 1.04/1.23 ((~(elem!1 = s(elem!1))) <=> (~(elem!1 = s(z)))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[5334])).
% 1.04/1.23 tff(5336,plain,
% 1.04/1.23 (~(elem!1 = s(z))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[46, 5335])).
% 1.04/1.23 tff(5337,plain,
% 1.04/1.23 ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) <=> (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[5250])).
% 1.04/1.23 tff(5338,assumption,(s(s(elem!1)) = s(s(s(s(s(elem!1)))))), introduced(assumption)).
% 1.04/1.23 tff(5339,plain,
% 1.04/1.23 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.04/1.23 inference(symmetry,[status(thm)],[5338])).
% 1.04/1.23 tff(5340,plain,
% 1.04/1.23 (s(s(s(s(s(elem!1))))) = s(s(z))),
% 1.04/1.23 inference(transitivity,[status(thm)],[5339, 4071])).
% 1.04/1.23 tff(5341,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2650, 5340])).
% 1.04/1.23 tff(5342,plain,((~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(5343,plain,
% 1.04/1.23 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5342, 97])).
% 1.04/1.23 tff(5344,plain,
% 1.04/1.23 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4895, 180, 5249, 5325])).
% 1.04/1.23 tff(5345,plain,
% 1.04/1.23 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[577, 150, 5344, 83])).
% 1.04/1.23 tff(5346,assumption,(~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.04/1.23 tff(5347,assumption,(r(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.04/1.23 tff(5348,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5349,plain,
% 1.04/1.23 (((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5350,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[5349])).
% 1.04/1.23 tff(5351,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[5350, 5348])).
% 1.04/1.23 tff(5352,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(5353,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[5352, 5351])).
% 1.04/1.23 tff(5354,plain,
% 1.04/1.23 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5353, 180, 254, 5347])).
% 1.04/1.23 tff(5355,plain,
% 1.04/1.23 (b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4115, 150, 5354, 5346])).
% 1.04/1.23 tff(5356,plain,
% 1.04/1.23 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5291, 180, 304, 5347])).
% 1.04/1.23 tff(5357,plain,
% 1.04/1.23 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2431, 5356, 2979])).
% 1.04/1.23 tff(5358,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5359,plain,
% 1.04/1.23 (((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5360,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[5359])).
% 1.04/1.23 tff(5361,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[5360, 5358])).
% 1.04/1.23 tff(5362,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(5363,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[5362, 5361])).
% 1.04/1.23 tff(5364,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5363, 206, 5357, 751, 5355])).
% 1.04/1.23 tff(5365,plain,((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(5366,plain,
% 1.04/1.23 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5365, 5345, 5343, 4090, 5249, 5325])).
% 1.04/1.23 tff(5367,plain,
% 1.04/1.23 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[5366, 5337])).
% 1.04/1.23 tff(5368,plain,
% 1.04/1.23 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2578, 5367])).
% 1.04/1.23 tff(5369,plain,
% 1.04/1.23 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5264, 180, 4274, 255])).
% 1.04/1.23 tff(5370,plain,
% 1.04/1.23 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4409, 150, 4380, 5369])).
% 1.04/1.23 tff(5371,plain,
% 1.04/1.23 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[3019, 4104])).
% 1.04/1.23 tff(5372,plain,
% 1.04/1.23 (~r(elem!1, s(z))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[3694, 255, 781])).
% 1.04/1.23 tff(5373,plain,
% 1.04/1.23 (b(elem!1, s(z))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[154, 5372, 65])).
% 1.04/1.23 tff(5374,plain,
% 1.04/1.23 (b(elem!1, s(elem!1))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[5373, 5253])).
% 1.04/1.23 tff(5375,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5376,plain,
% 1.04/1.23 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5377,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[5376])).
% 1.04/1.23 tff(5378,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[5377, 5375])).
% 1.04/1.23 tff(5379,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(5380,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[5379, 5378])).
% 1.04/1.23 tff(5381,plain,
% 1.04/1.23 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5380, 206, 5374, 5371])).
% 1.04/1.23 tff(5382,plain,
% 1.04/1.23 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2377, 5381, 4050])).
% 1.04/1.23 tff(5383,plain,
% 1.04/1.23 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[4287, 5382, 4089, 4274])).
% 1.04/1.23 tff(5384,plain,
% 1.04/1.23 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[3033, 5383, 4091])).
% 1.04/1.23 tff(5385,plain,
% 1.04/1.23 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[3028, 5384, 3019])).
% 1.04/1.23 tff(5386,plain,
% 1.04/1.23 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1402, 5385])).
% 1.04/1.23 tff(5387,plain,
% 1.04/1.23 (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1413, 5386, 243])).
% 1.04/1.23 tff(5388,plain,
% 1.04/1.23 (b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1088, 5387, 4080])).
% 1.04/1.23 tff(5389,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5390,plain,
% 1.04/1.23 (((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5391,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[5390])).
% 1.04/1.23 tff(5392,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[5391, 5389])).
% 1.04/1.23 tff(5393,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.23 inference(quant_inst,[status(thm)],[])).
% 1.04/1.23 tff(5394,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[5393, 5392])).
% 1.04/1.23 tff(5395,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5394, 206, 5388, 632, 5370])).
% 1.04/1.23 tff(5396,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~r(s(s(s(elem!1))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~(s(z) = s(elem!1))) | (elem!1 = s(z)) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(5397,plain,
% 1.04/1.23 (~r(s(s(elem!1)), elem!1)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5396, 5327, 5202, 5368, 5247, 97, 5336, 5330])).
% 1.04/1.23 tff(5398,plain,
% 1.04/1.23 (b(s(s(elem!1)), elem!1)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[267, 150, 5397, 30])).
% 1.04/1.23 tff(5399,plain,
% 1.04/1.23 ($false),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[327, 206, 654, 5398, 5327])).
% 1.04/1.23 tff(5400,plain,((~b(s(s(s(elem!1))), elem!1)) | (~(s(z) = s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.23 tff(5401,plain,
% 1.04/1.23 (~b(s(s(s(elem!1))), elem!1)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[5400, 5184, 11, 4472])).
% 1.04/1.23 tff(5402,plain,
% 1.04/1.23 (r(s(s(s(elem!1))), elem!1)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[320, 5401, 58])).
% 1.04/1.23 tff(5403,plain,
% 1.04/1.23 (b(s(z), z) <=> b(s(elem!1), z)),
% 1.04/1.23 inference(monotonicity,[status(thm)],[5184])).
% 1.04/1.23 tff(5404,plain,
% 1.04/1.23 (b(s(elem!1), z) <=> b(s(z), z)),
% 1.04/1.23 inference(symmetry,[status(thm)],[5403])).
% 1.04/1.23 tff(5405,plain,
% 1.04/1.23 (b(s(elem!1), z) <=> b(s(elem!1), elem!1)),
% 1.04/1.23 inference(monotonicity,[status(thm)],[5188])).
% 1.04/1.23 tff(5406,plain,
% 1.04/1.23 (b(s(elem!1), elem!1) <=> b(s(elem!1), z)),
% 1.04/1.23 inference(symmetry,[status(thm)],[5405])).
% 1.04/1.23 tff(5407,plain,
% 1.04/1.23 (b(s(elem!1), elem!1) <=> b(s(z), z)),
% 1.04/1.23 inference(transitivity,[status(thm)],[5406, 5404])).
% 1.04/1.23 tff(5408,plain,
% 1.04/1.23 (b(s(z), z)),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[4472, 5407])).
% 1.04/1.23 tff(5409,plain,
% 1.04/1.23 (b(s(elem!1), z)),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[4472, 5406])).
% 1.04/1.23 tff(5410,plain,
% 1.04/1.23 (r(s(s(s(elem!1))), z) <=> r(s(s(s(elem!1))), elem!1)),
% 1.04/1.23 inference(monotonicity,[status(thm)],[112])).
% 1.04/1.23 tff(5411,plain,
% 1.04/1.23 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(elem!1))), z)),
% 1.04/1.23 inference(symmetry,[status(thm)],[5410])).
% 1.04/1.23 tff(5412,plain,
% 1.04/1.23 (r(s(s(s(elem!1))), z)),
% 1.04/1.23 inference(modus_ponens,[status(thm)],[302, 5411])).
% 1.04/1.23 tff(5413,plain,
% 1.04/1.23 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1064, 1056, 796])).
% 1.04/1.23 tff(5414,plain,
% 1.04/1.23 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1562, 5413])).
% 1.04/1.23 tff(5415,plain,
% 1.04/1.23 (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[2107, 5414, 60])).
% 1.04/1.23 tff(5416,plain,
% 1.04/1.23 (b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.23 inference(unit_resolution,[status(thm)],[1088, 5415, 4080])).
% 1.04/1.23 tff(5417,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5418,plain,
% 1.04/1.23 (((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.04/1.23 inference(rewrite,[status(thm)],[])).
% 1.04/1.23 tff(5419,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 1.04/1.23 inference(monotonicity,[status(thm)],[5418])).
% 1.04/1.23 tff(5420,plain,
% 1.04/1.23 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.04/1.23 inference(transitivity,[status(thm)],[5419, 5417])).
% 1.04/1.23 tff(5421,plain,
% 1.04/1.23 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(5422,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5421, 5420])).
% 1.04/1.24 tff(5423,plain,
% 1.04/1.24 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5422, 206, 61, 5416])).
% 1.04/1.24 tff(5424,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5423, 4221])).
% 1.04/1.24 tff(5425,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~(s(z) = s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(5426,plain,
% 1.04/1.24 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5425, 61, 97, 5412, 796])).
% 1.04/1.24 tff(5427,plain,
% 1.04/1.24 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[1402, 5426])).
% 1.04/1.24 tff(5428,plain,
% 1.04/1.24 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5427, 5294])).
% 1.04/1.24 tff(5429,plain,
% 1.04/1.24 (~(s(s(elem!1)) = s(elem!1))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[56, 54])).
% 1.04/1.24 tff(5430,plain,
% 1.04/1.24 (r(s(s(elem!1)), s(elem!1))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[605, 897, 5429])).
% 1.04/1.24 tff(5431,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5432,plain,
% 1.04/1.24 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5433,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[5432])).
% 1.04/1.24 tff(5434,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[5433, 5431])).
% 1.04/1.24 tff(5435,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(5436,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5435, 5434])).
% 1.04/1.24 tff(5437,plain,
% 1.04/1.24 (~r(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5436, 180, 254, 5347])).
% 1.04/1.24 tff(5438,plain,
% 1.04/1.24 ((s(s(s(s(s(elem!1))))) = s(s(elem!1))) | b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4191, 150, 5437])).
% 1.04/1.24 tff(5439,plain,
% 1.04/1.24 (b(s(s(s(s(s(elem!1))))), s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5438, 4166])).
% 1.04/1.24 tff(5440,plain,
% 1.04/1.24 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(commutativity,[status(thm)],[])).
% 1.04/1.24 tff(5441,plain,
% 1.04/1.24 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.04/1.24 inference(symmetry,[status(thm)],[5440])).
% 1.04/1.24 tff(5442,plain,
% 1.04/1.24 ((~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[5441])).
% 1.04/1.24 tff(5443,plain,
% 1.04/1.24 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[4380, 5442])).
% 1.04/1.24 tff(5444,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5445,plain,
% 1.04/1.24 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5446,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[5445])).
% 1.04/1.24 tff(5447,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[5446, 5444])).
% 1.04/1.24 tff(5448,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(5449,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5448, 5447])).
% 1.04/1.24 tff(5450,plain,
% 1.04/1.24 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5449, 180, 254, 4381])).
% 1.04/1.24 tff(5451,plain,
% 1.04/1.24 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4231, 150, 5450])).
% 1.04/1.24 tff(5452,plain,
% 1.04/1.24 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5451, 5443])).
% 1.04/1.24 tff(5453,plain,
% 1.04/1.24 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5313, 180, 4381, 5347])).
% 1.04/1.24 tff(5454,plain,
% 1.04/1.24 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[3033, 5453, 4091])).
% 1.04/1.24 tff(5455,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5456,plain,
% 1.04/1.24 (((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5457,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[5456])).
% 1.04/1.24 tff(5458,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[5457, 5455])).
% 1.04/1.24 tff(5459,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(5460,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(elem!1))))), s(s(elem!1))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5459, 5458])).
% 1.04/1.24 tff(5461,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5460, 206, 5454, 5452, 5439])).
% 1.04/1.24 tff(5462,plain,((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~(s(z) = s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(5463,plain,
% 1.04/1.24 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5462, 5430, 97, 4381])).
% 1.04/1.24 tff(5464,plain,
% 1.04/1.24 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5463, 5337])).
% 1.04/1.24 tff(5465,plain,
% 1.04/1.24 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2578, 5464])).
% 1.04/1.24 tff(5466,plain,
% 1.04/1.24 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5465, 4104])).
% 1.04/1.24 tff(5467,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5468,plain,
% 1.04/1.24 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5469,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[5468])).
% 1.04/1.24 tff(5470,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[5469, 5467])).
% 1.04/1.24 tff(5471,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(5472,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5471, 5470])).
% 1.04/1.24 tff(5473,plain,
% 1.04/1.24 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5472, 206, 61, 5466])).
% 1.04/1.24 tff(5474,plain,
% 1.04/1.24 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2431, 5473, 4090])).
% 1.04/1.24 tff(5475,plain,
% 1.04/1.24 (b(s(s(elem!1)), elem!1)),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[196, 4176])).
% 1.04/1.24 tff(5476,plain,
% 1.04/1.24 (~r(elem!1, s(elem!1))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[4411, 5475, 4381, 5430, 4135, 4380])).
% 1.04/1.24 tff(5477,plain,
% 1.04/1.24 (b(elem!1, s(elem!1))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[401, 5476, 54])).
% 1.04/1.24 tff(5478,plain,
% 1.04/1.24 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5380, 206, 5477, 5466])).
% 1.04/1.24 tff(5479,plain,
% 1.04/1.24 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2377, 5478, 4050])).
% 1.04/1.24 tff(5480,plain,
% 1.04/1.24 ((~(s(s(s(s(s(elem!1))))) = z)) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[4047])).
% 1.04/1.24 tff(5481,plain,
% 1.04/1.24 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[1395, 5480])).
% 1.04/1.24 tff(5482,plain,
% 1.04/1.24 (b(elem!1, s(z))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5477, 5254])).
% 1.04/1.24 tff(5483,plain,
% 1.04/1.24 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[3498, 5465, 5482])).
% 1.04/1.24 tff(5484,plain,
% 1.04/1.24 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[3488, 5483, 5481])).
% 1.04/1.24 tff(5485,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5486,plain,
% 1.04/1.24 (((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5487,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[5486])).
% 1.04/1.24 tff(5488,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[5487, 5485])).
% 1.04/1.24 tff(5489,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(s(s(elem!1))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(5490,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(elem!1)))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5489, 5488])).
% 1.04/1.24 tff(5491,plain,
% 1.04/1.24 (~b(elem!1, s(s(s(elem!1))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5490, 206, 5477, 61])).
% 1.04/1.24 tff(5492,plain,
% 1.04/1.24 (r(elem!1, s(s(s(elem!1))))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[533, 5491, 508])).
% 1.04/1.24 tff(5493,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5494,plain,
% 1.04/1.24 (((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1)))))))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5495,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[5494])).
% 1.04/1.24 tff(5496,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[5495, 5493])).
% 1.04/1.24 tff(5497,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(elem!1, s(s(s(s(s(elem!1))))))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(5498,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5497, 5496])).
% 1.04/1.24 tff(5499,plain,
% 1.04/1.24 ($false),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5498, 180, 5492, 5484, 5479, 5474])).
% 1.04/1.24 tff(5500,plain,((~b(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~(s(z) = s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = s(elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.24 tff(5501,plain,
% 1.04/1.24 (~b(s(s(elem!1)), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5500, 61, 97, 5428, 508, 54, 95])).
% 1.04/1.24 tff(5502,plain,
% 1.04/1.24 (r(s(s(elem!1)), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[228, 5501])).
% 1.04/1.24 tff(5503,plain,
% 1.04/1.24 (r(s(s(elem!1)), elem!1)),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5502, 4067])).
% 1.04/1.24 tff(5504,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5505,plain,
% 1.04/1.24 (((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5506,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[5505])).
% 1.04/1.24 tff(5507,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[5506, 5504])).
% 1.04/1.24 tff(5508,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1)))))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(5509,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(elem!1))), s(s(elem!1))))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5508, 5507])).
% 1.04/1.24 tff(5510,plain,
% 1.04/1.24 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5509, 180, 302, 5503])).
% 1.04/1.24 tff(5511,plain,
% 1.04/1.24 (~(elem!1 = s(z))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[54, 5335])).
% 1.04/1.24 tff(5512,plain,
% 1.04/1.24 (~(s(s(s(elem!1))) = s(s(elem!1)))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[76, 5429])).
% 1.04/1.24 tff(5513,plain,
% 1.04/1.24 (b(s(s(s(z))), s(z))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[61, 4054])).
% 1.04/1.24 tff(5514,plain,
% 1.04/1.24 (r(s(s(s(z))), z) <=> r(s(s(s(z))), elem!1)),
% 1.04/1.24 inference(monotonicity,[status(thm)],[112])).
% 1.04/1.24 tff(5515,plain,
% 1.04/1.24 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), z)),
% 1.04/1.24 inference(symmetry,[status(thm)],[5514])).
% 1.04/1.24 tff(5516,plain,
% 1.04/1.24 (r(s(s(s(z))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 1.04/1.24 inference(monotonicity,[status(thm)],[4052])).
% 1.04/1.24 tff(5517,plain,
% 1.04/1.24 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), elem!1)),
% 1.04/1.24 inference(symmetry,[status(thm)],[5516])).
% 1.04/1.24 tff(5518,plain,
% 1.04/1.24 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(z))), z)),
% 1.04/1.24 inference(transitivity,[status(thm)],[5517, 5515])).
% 1.04/1.24 tff(5519,plain,
% 1.04/1.24 (r(s(s(s(z))), z)),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[302, 5518])).
% 1.04/1.24 tff(5520,plain,
% 1.04/1.24 (r(s(s(z)), z) <=> r(s(s(z)), elem!1)),
% 1.04/1.24 inference(monotonicity,[status(thm)],[112])).
% 1.04/1.24 tff(5521,plain,
% 1.04/1.24 (r(s(s(z)), elem!1) <=> r(s(s(z)), z)),
% 1.04/1.24 inference(symmetry,[status(thm)],[5520])).
% 1.04/1.24 tff(5522,plain,
% 1.04/1.24 (r(s(s(elem!1)), z) <=> r(s(s(z)), z)),
% 1.04/1.24 inference(transitivity,[status(thm)],[4067, 4066, 5521])).
% 1.04/1.24 tff(5523,plain,
% 1.04/1.24 (r(s(s(z)), z)),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[241, 5522])).
% 1.04/1.24 tff(5524,plain,
% 1.04/1.24 (~r(z, s(z))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[2150, 5523, 4342])).
% 1.04/1.24 tff(5525,plain,
% 1.04/1.24 (b(z, s(z))),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[505, 5524])).
% 1.04/1.24 tff(5526,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5527,plain,
% 1.04/1.24 (((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.04/1.24 inference(rewrite,[status(thm)],[])).
% 1.04/1.24 tff(5528,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 1.04/1.24 inference(monotonicity,[status(thm)],[5527])).
% 1.04/1.24 tff(5529,plain,
% 1.04/1.24 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.04/1.24 inference(transitivity,[status(thm)],[5528, 5526])).
% 1.04/1.24 tff(5530,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 1.04/1.24 inference(quant_inst,[status(thm)],[])).
% 1.04/1.24 tff(5531,plain,
% 1.04/1.24 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.04/1.24 inference(modus_ponens,[status(thm)],[5530, 5529])).
% 1.04/1.24 tff(5532,plain,
% 1.04/1.24 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.04/1.24 inference(unit_resolution,[status(thm)],[5531, 206, 1056, 911])).
% 1.04/1.24 tff(5533,plain,
% 1.04/1.24 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1560, 150, 1557, 5532])).
% 1.04/1.25 tff(5534,plain,
% 1.04/1.25 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1379, 150, 3335, 1341])).
% 1.04/1.25 tff(5535,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), z)))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5536,plain,
% 1.04/1.25 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), z)))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5537,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), z))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[5536])).
% 1.04/1.25 tff(5538,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), z)))),
% 1.04/1.25 inference(transitivity,[status(thm)],[5537, 5535])).
% 1.04/1.25 tff(5539,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(5540,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(z))), z))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5539, 5538])).
% 1.04/1.25 tff(5541,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5540, 180, 5534, 5533, 2041])).
% 1.04/1.25 tff(5542,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(z))), z)) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(5543,plain,
% 1.04/1.25 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5542, 5525, 5519, 5513])).
% 1.04/1.25 tff(5544,plain,
% 1.04/1.25 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1402, 5543])).
% 1.04/1.25 tff(5545,plain,
% 1.04/1.25 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5544, 5294])).
% 1.04/1.25 tff(5546,plain,
% 1.04/1.25 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5449, 180, 254, 5545])).
% 1.04/1.25 tff(5547,plain,
% 1.04/1.25 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4231, 150, 5546])).
% 1.04/1.25 tff(5548,plain,
% 1.04/1.25 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5547, 5443])).
% 1.04/1.25 tff(5549,plain,
% 1.04/1.25 (r(s(s(elem!1)), elem!1)),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[241, 4067])).
% 1.04/1.25 tff(5550,plain,
% 1.04/1.25 (~r(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5509, 180, 302, 5549])).
% 1.04/1.25 tff(5551,plain,
% 1.04/1.25 (b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[331, 150, 80, 5550])).
% 1.04/1.25 tff(5552,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5553,plain,
% 1.04/1.25 (((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5554,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[5553])).
% 1.04/1.25 tff(5555,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[5554, 5552])).
% 1.04/1.25 tff(5556,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(5557,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5556, 5555])).
% 1.04/1.25 tff(5558,plain,
% 1.04/1.25 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5557, 206, 61, 5551, 5548])).
% 1.04/1.25 tff(5559,plain,
% 1.04/1.25 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[1365, 5558, 4213])).
% 1.04/1.25 tff(5560,plain,
% 1.04/1.25 (~r(elem!1, s(z))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[3699, 5549, 4544, 302])).
% 1.04/1.25 tff(5561,plain,
% 1.04/1.25 (b(elem!1, s(z))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[154, 5560, 65])).
% 1.04/1.25 tff(5562,plain,
% 1.04/1.25 (b(elem!1, s(elem!1))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5561, 5253])).
% 1.04/1.25 tff(5563,plain,
% 1.04/1.25 (~b(elem!1, s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5490, 206, 5562, 61])).
% 1.04/1.25 tff(5564,plain,
% 1.04/1.25 (r(elem!1, s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[533, 5563, 508])).
% 1.04/1.25 tff(5565,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5566,plain,
% 1.04/1.25 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5567,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[5566])).
% 1.04/1.25 tff(5568,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[5567, 5565])).
% 1.04/1.25 tff(5569,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(5570,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5569, 5568])).
% 1.04/1.25 tff(5571,plain,
% 1.04/1.25 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5570, 180, 5564, 5559])).
% 1.04/1.25 tff(5572,plain,
% 1.04/1.25 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[3090, 5571, 4135])).
% 1.04/1.25 tff(5573,plain,
% 1.04/1.25 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[588, 241, 5412])).
% 1.04/1.25 tff(5574,plain,
% 1.04/1.25 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[577, 150, 5573, 4544])).
% 1.04/1.25 tff(5575,plain,
% 1.04/1.25 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5313, 180, 4381])).
% 1.04/1.25 tff(5576,plain,
% 1.04/1.25 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5575, 5347])).
% 1.04/1.25 tff(5577,plain,
% 1.04/1.25 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[3033, 5576, 4091])).
% 1.04/1.25 tff(5578,plain,
% 1.04/1.25 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[3383, 5577, 3375])).
% 1.04/1.25 tff(5579,plain,
% 1.04/1.25 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[2377, 5578, 4050])).
% 1.04/1.25 tff(5580,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5581,plain,
% 1.04/1.25 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5582,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[5581])).
% 1.04/1.25 tff(5583,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[5582, 5580])).
% 1.04/1.25 tff(5584,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(5585,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5584, 5583])).
% 1.04/1.25 tff(5586,plain,
% 1.04/1.25 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5585, 180, 302, 5579])).
% 1.04/1.25 tff(5587,plain,
% 1.04/1.25 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[2431, 5586, 4090])).
% 1.04/1.25 tff(5588,plain,
% 1.04/1.25 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5363, 206, 5587, 751])).
% 1.04/1.25 tff(5589,plain,
% 1.04/1.25 ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1)))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5353, 180, 254])).
% 1.04/1.25 tff(5590,plain,
% 1.04/1.25 (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5589, 5347])).
% 1.04/1.25 tff(5591,plain,
% 1.04/1.25 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4115, 150, 5590])).
% 1.04/1.25 tff(5592,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5591, 5588, 4076])).
% 1.04/1.25 tff(5593,plain,((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~(s(z) = s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(5594,plain,
% 1.04/1.25 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5593, 5574, 97, 302, 5572, 5545, 254])).
% 1.04/1.25 tff(5595,plain,
% 1.04/1.25 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5594, 5337])).
% 1.04/1.25 tff(5596,plain,
% 1.04/1.25 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[2578, 5595])).
% 1.04/1.25 tff(5597,plain,
% 1.04/1.25 (b(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5596, 4104])).
% 1.04/1.25 tff(5598,plain,
% 1.04/1.25 (~b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5472, 206, 61, 5597])).
% 1.04/1.25 tff(5599,plain,
% 1.04/1.25 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[2431, 5598, 4090])).
% 1.04/1.25 tff(5600,plain,
% 1.04/1.25 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5380, 206, 5562, 5597])).
% 1.04/1.25 tff(5601,plain,
% 1.04/1.25 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[2377, 5600, 4050])).
% 1.04/1.25 tff(5602,plain,
% 1.04/1.25 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[3498, 5596, 5561])).
% 1.04/1.25 tff(5603,plain,
% 1.04/1.25 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[3488, 5602, 5481])).
% 1.04/1.25 tff(5604,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5498, 180, 5564, 5603, 5601, 5599])).
% 1.04/1.25 tff(5605,plain,((~r(s(s(elem!1)), z)) | (~b(s(s(s(elem!1))), s(elem!1))) | (~(s(z) = s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (s(s(s(elem!1))) = s(s(elem!1))) | (elem!1 = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(5606,plain,
% 1.04/1.25 (~r(s(s(elem!1)), s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5605, 5502, 97, 302, 61, 508, 5512, 5511])).
% 1.04/1.25 tff(5607,plain,
% 1.04/1.25 (b(s(s(elem!1)), s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[605, 5606, 5429])).
% 1.04/1.25 tff(5608,plain,
% 1.04/1.25 (~b(s(s(s(elem!1))), s(s(elem!1)))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[640, 5607, 61])).
% 1.04/1.25 tff(5609,plain,
% 1.04/1.25 ($false),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[331, 150, 5512, 5608, 5510])).
% 1.04/1.25 tff(5610,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~(s(z) = s(elem!1))) | (elem!1 = s(s(s(elem!1)))) | (elem!1 = s(elem!1)) | (~b(s(elem!1), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.25 tff(5611,plain,
% 1.04/1.25 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5610, 5402, 5184, 419, 46, 5409, 5408])).
% 1.04/1.25 tff(5612,plain,
% 1.04/1.25 (r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[293, 5611, 11])).
% 1.04/1.25 tff(5613,plain,
% 1.04/1.25 (~r(elem!1, s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4966, 5612, 5402])).
% 1.04/1.25 tff(5614,plain,
% 1.04/1.25 (b(elem!1, s(elem!1))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[401, 5613, 46])).
% 1.04/1.25 tff(5615,plain,
% 1.04/1.25 (b(z, s(z))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5614, 5191])).
% 1.04/1.25 tff(5616,plain,
% 1.04/1.25 (b(elem!1, s(z)) <=> b(elem!1, s(elem!1))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[5184])).
% 1.04/1.25 tff(5617,plain,
% 1.04/1.25 (b(elem!1, s(elem!1)) <=> b(elem!1, s(z))),
% 1.04/1.25 inference(symmetry,[status(thm)],[5616])).
% 1.04/1.25 tff(5618,plain,
% 1.04/1.25 (b(elem!1, s(z))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5614, 5617])).
% 1.04/1.25 tff(5619,plain,
% 1.04/1.25 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5282, 5252, 157, 4050, 4088])).
% 1.04/1.25 tff(5620,plain,
% 1.04/1.25 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[2578, 5619])).
% 1.04/1.25 tff(5621,plain,
% 1.04/1.25 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5620, 5251])).
% 1.04/1.25 tff(5622,plain,
% 1.04/1.25 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.04/1.25 inference(symmetry,[status(thm)],[4052])).
% 1.04/1.25 tff(5623,plain,
% 1.04/1.25 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))) <=> b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[5622])).
% 1.04/1.25 tff(5624,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5625,plain,
% 1.04/1.25 (((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1)))))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5626,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[5625])).
% 1.04/1.25 tff(5627,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[5626, 5624])).
% 1.04/1.25 tff(5628,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(5629,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5628, 5627])).
% 1.04/1.25 tff(5630,plain,
% 1.04/1.25 (~r(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5629, 180, 304, 5621])).
% 1.04/1.25 tff(5631,plain,
% 1.04/1.25 ((s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))) | b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4438, 150, 5630])).
% 1.04/1.25 tff(5632,plain,
% 1.04/1.25 (b(s(s(s(elem!1))), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5631, 4428])).
% 1.04/1.25 tff(5633,plain,
% 1.04/1.25 (b(s(s(s(z))), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5632, 5623])).
% 1.04/1.25 tff(5634,plain,
% 1.04/1.25 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[588, 229, 5412])).
% 1.04/1.25 tff(5635,plain,
% 1.04/1.25 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[577, 150, 5634, 3679])).
% 1.04/1.25 tff(5636,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5637,plain,
% 1.04/1.25 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5638,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[5637])).
% 1.04/1.25 tff(5639,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))))),
% 1.04/1.25 inference(transitivity,[status(thm)],[5638, 5636])).
% 1.04/1.25 tff(5640,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))))),
% 1.04/1.25 inference(quant_inst,[status(thm)],[])).
% 1.04/1.25 tff(5641,plain,
% 1.04/1.25 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(elem!1))))), s(elem!1)))),
% 1.04/1.25 inference(modus_ponens,[status(thm)],[5640, 5639])).
% 1.04/1.25 tff(5642,plain,
% 1.04/1.25 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5641, 180, 302, 304, 5621])).
% 1.04/1.25 tff(5643,plain,
% 1.04/1.25 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[2431, 5642, 4090])).
% 1.04/1.25 tff(5644,plain,
% 1.04/1.25 (~b(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5363, 206, 5643, 5635])).
% 1.04/1.25 tff(5645,plain,
% 1.04/1.25 ((s(s(elem!1)) = s(s(s(s(s(elem!1)))))) | r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[4115, 150, 5644])).
% 1.04/1.25 tff(5646,plain,
% 1.04/1.25 (r(s(s(elem!1)), s(s(s(s(s(elem!1))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[5645, 4076])).
% 1.04/1.25 tff(5647,assumption,(r(s(s(elem!1)), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.04/1.25 tff(5648,assumption,(b(s(s(s(z))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.04/1.25 tff(5649,plain,
% 1.04/1.25 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.25 inference(unit_resolution,[status(thm)],[3340, 5416, 102])).
% 1.04/1.25 tff(5650,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5651,plain,
% 1.04/1.25 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.04/1.25 inference(rewrite,[status(thm)],[])).
% 1.04/1.25 tff(5652,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))))),
% 1.04/1.25 inference(monotonicity,[status(thm)],[5651])).
% 1.04/1.25 tff(5653,plain,
% 1.04/1.25 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5652, 5650])).
% 1.04/1.26 tff(5654,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5655,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5654, 5653])).
% 1.04/1.26 tff(5656,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5655, 206, 3020, 1681, 5648])).
% 1.04/1.26 tff(5657,plain,((~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(5658,plain,
% 1.04/1.26 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5657, 5649, 5648])).
% 1.04/1.26 tff(5659,plain,
% 1.04/1.26 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[3033, 5658, 4091])).
% 1.04/1.26 tff(5660,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5661,plain,
% 1.04/1.26 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5662,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5661])).
% 1.04/1.26 tff(5663,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5662, 5660])).
% 1.04/1.26 tff(5664,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5665,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5664, 5663])).
% 1.04/1.26 tff(5666,plain,
% 1.04/1.26 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5665, 180, 5659, 5647])).
% 1.04/1.26 tff(5667,plain,
% 1.04/1.26 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4409, 150, 4380, 5666])).
% 1.04/1.26 tff(5668,plain,
% 1.04/1.26 ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5273, 206, 195])).
% 1.04/1.26 tff(5669,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5668, 5667, 4221])).
% 1.04/1.26 tff(5670,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~(s(z) = s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(z))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(elem!1))), z)) | (~b(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(5671,plain,
% 1.04/1.26 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5670, 195, 97, 5646, 5633, 5412, 796])).
% 1.04/1.26 tff(5672,plain,
% 1.04/1.26 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1402, 5671])).
% 1.04/1.26 tff(5673,plain,
% 1.04/1.26 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5298, 5672, 97])).
% 1.04/1.26 tff(5674,plain,
% 1.04/1.26 (~r(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1413, 5672, 4083])).
% 1.04/1.26 tff(5675,plain,
% 1.04/1.26 (b(s(s(s(elem!1))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1088, 5674, 4080])).
% 1.04/1.26 tff(5676,plain,
% 1.04/1.26 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[3340, 5675, 102])).
% 1.04/1.26 tff(5677,plain,
% 1.04/1.26 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5657, 5676, 5633])).
% 1.04/1.26 tff(5678,plain,
% 1.04/1.26 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[3033, 5677, 4091])).
% 1.04/1.26 tff(5679,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5313, 180, 5678, 5673, 5621])).
% 1.04/1.26 tff(5680,plain,((~b(s(s(elem!1)), s(elem!1))) | (~(s(z) = s(elem!1))) | (~b(s(z), z)) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~b(elem!1, s(z))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(5681,plain,
% 1.04/1.26 (~b(s(s(elem!1)), s(elem!1))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5680, 5618, 5408, 5184, 5402, 83, 5612, 5409])).
% 1.04/1.26 tff(5682,plain,
% 1.04/1.26 (r(s(s(elem!1)), s(elem!1))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[605, 5681, 57])).
% 1.04/1.26 tff(5683,plain,
% 1.04/1.26 (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[2881, 5187])).
% 1.04/1.26 tff(5684,plain,
% 1.04/1.26 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5683, 1346])).
% 1.04/1.26 tff(5685,plain,
% 1.04/1.26 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4379, 5184])).
% 1.04/1.26 tff(5686,plain,
% 1.04/1.26 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5010, 180, 5402, 5612, 5682])).
% 1.04/1.26 tff(5687,plain,
% 1.04/1.26 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[577, 150, 5686, 83])).
% 1.04/1.26 tff(5688,plain,
% 1.04/1.26 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4403, 180, 254, 4381])).
% 1.04/1.26 tff(5689,plain,
% 1.04/1.26 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4409, 150, 4406, 5688])).
% 1.04/1.26 tff(5690,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))), introduced(assumption)).
% 1.04/1.26 tff(5691,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5692,plain,
% 1.04/1.26 (((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5693,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5692])).
% 1.04/1.26 tff(5694,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5693, 5691])).
% 1.04/1.26 tff(5695,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5696,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5695, 5694])).
% 1.04/1.26 tff(5697,plain,
% 1.04/1.26 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5696, 180, 302, 304, 4381])).
% 1.04/1.26 tff(5698,plain,
% 1.04/1.26 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1365, 5697, 5690])).
% 1.04/1.26 tff(5699,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5700,plain,
% 1.04/1.26 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5701,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5700])).
% 1.04/1.26 tff(5702,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5701, 5699])).
% 1.04/1.26 tff(5703,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5704,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5703, 5702])).
% 1.04/1.26 tff(5705,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5704, 206, 5698, 751, 5689])).
% 1.04/1.26 tff(5706,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(5707,plain,
% 1.04/1.26 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5706, 5687, 5685, 5684, 5402, 5612, 5682])).
% 1.04/1.26 tff(5708,plain,
% 1.04/1.26 (~r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5298, 5707, 5184])).
% 1.04/1.26 tff(5709,plain,
% 1.04/1.26 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1402, 5708])).
% 1.04/1.26 tff(5710,plain,
% 1.04/1.26 (elem!1 = z),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[137, 5188])).
% 1.04/1.26 tff(5711,plain,
% 1.04/1.26 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[2937, 5710])).
% 1.04/1.26 tff(5712,plain,
% 1.04/1.26 (~(s(s(elem!1)) = s(s(s(s(s(elem!1))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5342, 5184])).
% 1.04/1.26 tff(5713,plain,
% 1.04/1.26 (~r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5365, 5687, 5712, 5711, 5612, 5682])).
% 1.04/1.26 tff(5714,plain,
% 1.04/1.26 (r(s(s(s(s(s(elem!1))))), s(elem!1))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[2580, 5251])).
% 1.04/1.26 tff(5715,assumption,(~r(s(s(s(s(s(elem!1))))), s(elem!1))), introduced(assumption)).
% 1.04/1.26 tff(5716,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5715, 5714])).
% 1.04/1.26 tff(5717,plain,((~r(s(s(s(s(s(elem!1))))), s(z))) | r(s(s(s(s(s(elem!1))))), s(elem!1)) | (~(s(z) = s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(5718,plain,
% 1.04/1.26 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5717, 5713, 5184])).
% 1.04/1.26 tff(5719,plain,
% 1.04/1.26 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[2578, 5718])).
% 1.04/1.26 tff(5720,plain,
% 1.04/1.26 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[3028, 5719, 5709])).
% 1.04/1.26 tff(5721,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5722,plain,
% 1.04/1.26 (((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5723,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5722])).
% 1.04/1.26 tff(5724,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5723, 5721])).
% 1.04/1.26 tff(5725,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5726,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5725, 5724])).
% 1.04/1.26 tff(5727,plain,
% 1.04/1.26 (~b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5726, 206, 1056, 3019])).
% 1.04/1.26 tff(5728,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5729,plain,
% 1.04/1.26 (((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5730,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5729])).
% 1.04/1.26 tff(5731,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5730, 5728])).
% 1.04/1.26 tff(5732,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5733,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(elem!1))))), z))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5732, 5731])).
% 1.04/1.26 tff(5734,plain,
% 1.04/1.26 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5733, 206, 3019, 911])).
% 1.04/1.26 tff(5735,plain,
% 1.04/1.26 (r(s(s(s(s(s(elem!1))))), z)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[2388, 150, 1395, 5734])).
% 1.04/1.26 tff(5736,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5737,plain,
% 1.04/1.26 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5738,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5737])).
% 1.04/1.26 tff(5739,plain,
% 1.04/1.26 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5738, 5736])).
% 1.04/1.26 tff(5740,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5741,plain,
% 1.04/1.26 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(elem!1))))), z)) | (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5740, 5739])).
% 1.04/1.26 tff(5742,plain,
% 1.04/1.26 (~r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5741, 180, 5533, 5735])).
% 1.04/1.26 tff(5743,plain,
% 1.04/1.26 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))),
% 1.04/1.26 inference(rewrite,[status(thm)],[])).
% 1.04/1.26 tff(5744,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))))),
% 1.04/1.26 inference(quant_inst,[status(thm)],[])).
% 1.04/1.26 tff(5745,plain,
% 1.04/1.26 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(modus_ponens,[status(thm)],[5744, 5743])).
% 1.04/1.26 tff(5746,plain,
% 1.04/1.26 ((s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(elem!1))))), s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5745, 150])).
% 1.04/1.26 tff(5747,plain,
% 1.04/1.26 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5746, 5742, 5727])).
% 1.04/1.26 tff(5748,plain,
% 1.04/1.26 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[4284, 180, 5533, 5735])).
% 1.04/1.26 tff(5749,plain,
% 1.04/1.26 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(elem!1)))))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[3033, 5748, 4303])).
% 1.04/1.26 tff(5750,plain,
% 1.04/1.26 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[2981, 5749])).
% 1.04/1.26 tff(5751,plain,
% 1.04/1.26 (s(s(s(elem!1))) = s(s(s(s(s(elem!1)))))),
% 1.04/1.26 inference(symmetry,[status(thm)],[5750])).
% 1.04/1.26 tff(5752,plain,
% 1.04/1.26 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5751, 5747])).
% 1.04/1.26 tff(5753,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[1606, 5752])).
% 1.04/1.26 tff(5754,plain,((~b(z, s(z))) | (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) | (~b(s(s(s(s(s(elem!1))))), s(z))) | (~b(s(s(s(s(s(s(elem!1)))))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(5755,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5754, 5720, 5719, 5683, 5709, 5615])).
% 1.04/1.26 tff(5756,plain,((s(s(s(elem!1))) = elem!1) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(5757,plain,
% 1.04/1.26 (s(s(s(elem!1))) = elem!1),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5756, 11])).
% 1.04/1.26 tff(5758,plain,
% 1.04/1.26 (elem!1 = s(s(s(elem!1)))),
% 1.04/1.26 inference(symmetry,[status(thm)],[2883])).
% 1.04/1.26 tff(5759,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 1.04/1.26 tff(5760,plain,
% 1.04/1.26 (s(s(s(s(z)))) = s(s(s(elem!1)))),
% 1.04/1.26 inference(transitivity,[status(thm)],[5759, 5758])).
% 1.04/1.26 tff(5761,plain,
% 1.04/1.26 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5760])).
% 1.04/1.26 tff(5762,plain,
% 1.04/1.26 (s(s(s(z))) = s(s(elem!1))),
% 1.04/1.26 inference(transitivity,[status(thm)],[1031, 5761, 71])).
% 1.04/1.26 tff(5763,plain,
% 1.04/1.26 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5762])).
% 1.04/1.26 tff(5764,plain,
% 1.04/1.26 (s(s(z)) = s(elem!1)),
% 1.04/1.26 inference(transitivity,[status(thm)],[1036, 5763, 48])).
% 1.04/1.26 tff(5765,plain,
% 1.04/1.26 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5764])).
% 1.04/1.26 tff(5766,plain,
% 1.04/1.26 (s(z) = elem!1),
% 1.04/1.26 inference(transitivity,[status(thm)],[1332, 5765, 10])).
% 1.04/1.26 tff(5767,plain,
% 1.04/1.26 (s(z) = s(s(s(elem!1)))),
% 1.04/1.26 inference(transitivity,[status(thm)],[2368, 5758])).
% 1.04/1.26 tff(5768,plain,
% 1.04/1.26 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 1.04/1.26 inference(monotonicity,[status(thm)],[5767])).
% 1.04/1.26 tff(5769,plain,
% 1.04/1.26 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 1.04/1.26 inference(symmetry,[status(thm)],[5768])).
% 1.04/1.26 tff(5770,plain,
% 1.04/1.26 (s(s(elem!1)) = z),
% 1.04/1.26 inference(transitivity,[status(thm)],[72, 5769, 106])).
% 1.04/1.26 tff(5771,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[224, 5770])).
% 1.04/1.26 tff(5772,plain,((~(s(z) = elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.26 tff(5773,plain,
% 1.04/1.26 (~(s(z) = elem!1)),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5772, 2883])).
% 1.04/1.26 tff(5774,plain,
% 1.04/1.26 ($false),
% 1.04/1.26 inference(unit_resolution,[status(thm)],[5773, 5766])).
% 1.04/1.26 tff(5775,plain,((~(s(s(s(s(z)))) = elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(5776,plain,
% 1.04/1.27 (~(s(s(s(s(z)))) = elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5775, 5757])).
% 1.04/1.27 tff(5777,plain,
% 1.04/1.27 (~(s(z) = elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5772, 5757])).
% 1.04/1.27 tff(5778,plain,
% 1.04/1.27 (~(elem!1 = s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[162, 5777])).
% 1.04/1.27 tff(5779,plain,
% 1.04/1.27 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5757])).
% 1.04/1.27 tff(5780,plain,
% 1.04/1.27 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(elem!1, s(z)))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5779])).
% 1.04/1.27 tff(5781,plain,
% 1.04/1.27 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[2894, 5757])).
% 1.04/1.27 tff(5782,plain,
% 1.04/1.27 (~(s(elem!1) = s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[2881, 5781])).
% 1.04/1.27 tff(5783,plain,
% 1.04/1.27 (~(s(z) = s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[101, 5782])).
% 1.04/1.27 tff(5784,plain,
% 1.04/1.27 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.04/1.27 inference(symmetry,[status(thm)],[5781])).
% 1.04/1.27 tff(5785,plain,
% 1.04/1.27 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5784])).
% 1.04/1.27 tff(5786,plain,
% 1.04/1.27 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.04/1.27 inference(transitivity,[status(thm)],[1096, 5785, 71])).
% 1.04/1.27 tff(5787,plain,
% 1.04/1.27 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (elem!1 = s(s(elem!1)))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5786])).
% 1.04/1.27 tff(5788,plain,
% 1.04/1.27 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[5787])).
% 1.04/1.27 tff(5789,plain,
% 1.04/1.27 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.04/1.27 inference(transitivity,[status(thm)],[5788, 64])).
% 1.04/1.27 tff(5790,plain,
% 1.04/1.27 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5789])).
% 1.04/1.27 tff(5791,plain,
% 1.04/1.27 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[24, 5790])).
% 1.04/1.27 tff(5792,plain,
% 1.04/1.27 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5757])).
% 1.04/1.27 tff(5793,plain,
% 1.04/1.27 (b(elem!1, s(elem!1))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[61, 5792])).
% 1.04/1.27 tff(5794,plain,
% 1.04/1.27 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[5785])).
% 1.04/1.27 tff(5795,plain,
% 1.04/1.27 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[72, 5794, 1023])).
% 1.04/1.27 tff(5796,plain,
% 1.04/1.27 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5795])).
% 1.04/1.27 tff(5797,plain,
% 1.04/1.27 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.04/1.27 inference(symmetry,[status(thm)],[5796])).
% 1.04/1.27 tff(5798,plain,
% 1.04/1.27 (r(s(s(elem!1)), elem!1)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[2948, 5797])).
% 1.04/1.27 tff(5799,plain,
% 1.04/1.27 (~r(s(elem!1), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[263, 5798, 254])).
% 1.04/1.27 tff(5800,plain,
% 1.04/1.27 (b(s(elem!1), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[167, 5799, 38])).
% 1.04/1.27 tff(5801,plain,
% 1.04/1.27 (~(z = elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[239, 5782])).
% 1.04/1.27 tff(5802,assumption,(s(s(elem!1)) = s(s(s(s(z))))), introduced(assumption)).
% 1.04/1.27 tff(5803,plain,
% 1.04/1.27 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.04/1.27 inference(symmetry,[status(thm)],[5802])).
% 1.04/1.27 tff(5804,plain,
% 1.04/1.27 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5803])).
% 1.04/1.27 tff(5805,plain,
% 1.04/1.27 (s(s(s(z))) = s(elem!1)),
% 1.04/1.27 inference(transitivity,[status(thm)],[1031, 5804, 48])).
% 1.04/1.27 tff(5806,plain,
% 1.04/1.27 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5805])).
% 1.04/1.27 tff(5807,plain,
% 1.04/1.27 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[5806])).
% 1.04/1.27 tff(5808,plain,
% 1.04/1.27 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[2894, 2883])).
% 1.04/1.27 tff(5809,plain,
% 1.04/1.27 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 1.04/1.27 inference(symmetry,[status(thm)],[5808])).
% 1.04/1.27 tff(5810,plain,
% 1.04/1.27 (s(s(s(s(s(s(elem!1)))))) = s(s(z))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5809, 2883, 52, 5807, 1035])).
% 1.04/1.27 tff(5811,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1111, 5810])).
% 1.04/1.27 tff(5812,plain,((~(s(s(elem!1)) = s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(5813,plain,
% 1.04/1.27 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5812, 5757])).
% 1.04/1.27 tff(5814,assumption,(s(elem!1) = s(s(s(s(z))))), introduced(assumption)).
% 1.04/1.27 tff(5815,plain,
% 1.04/1.27 (s(s(s(s(z)))) = s(elem!1)),
% 1.04/1.27 inference(symmetry,[status(thm)],[5814])).
% 1.04/1.27 tff(5816,plain,
% 1.04/1.27 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5815])).
% 1.04/1.27 tff(5817,plain,
% 1.04/1.27 (inj_0(s(elem!1)) = inj_0(s(s(s(s(z)))))),
% 1.04/1.27 inference(symmetry,[status(thm)],[5816])).
% 1.04/1.27 tff(5818,plain,
% 1.04/1.27 (s(s(s(elem!1))) = s(s(s(z)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[2883, 52, 5817, 1030])).
% 1.04/1.27 tff(5819,plain,
% 1.04/1.27 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(z))) = s(s(s(elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5809])).
% 1.04/1.27 tff(5820,plain,
% 1.04/1.27 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(elem!1))) = s(s(s(z))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5819, 1750])).
% 1.04/1.27 tff(5821,plain,
% 1.04/1.27 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(elem!1))) = s(s(s(z)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5820])).
% 1.04/1.27 tff(5822,plain,
% 1.04/1.27 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[1341, 5821])).
% 1.04/1.27 tff(5823,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5822, 5818])).
% 1.04/1.27 tff(5824,plain,((~(s(elem!1) = s(s(s(s(z)))))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(5825,plain,
% 1.04/1.27 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5824, 5757])).
% 1.04/1.27 tff(5826,plain,
% 1.04/1.27 (~r(s(s(elem!1)), z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[278, 270, 254])).
% 1.04/1.27 tff(5827,plain,
% 1.04/1.27 (b(s(s(elem!1)), z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[228, 5826])).
% 1.04/1.27 tff(5828,assumption,(~(s(s(s(s(z)))) = elem!1)), introduced(assumption)).
% 1.04/1.27 tff(5829,plain,
% 1.04/1.27 (~r(s(elem!1), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[263, 255, 254])).
% 1.04/1.27 tff(5830,plain,
% 1.04/1.27 (b(s(elem!1), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[167, 5829, 43])).
% 1.04/1.27 tff(5831,assumption,(~(s(elem!1) = s(s(s(s(z)))))), introduced(assumption)).
% 1.04/1.27 tff(5832,plain,
% 1.04/1.27 (~r(s(s(elem!1)), s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[3694, 441, 255])).
% 1.04/1.27 tff(5833,plain,
% 1.04/1.27 (b(s(s(elem!1)), s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[778, 5832])).
% 1.04/1.27 tff(5834,plain,
% 1.04/1.27 (~b(z, s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[2363, 5833, 196])).
% 1.04/1.27 tff(5835,plain,
% 1.04/1.27 (r(z, s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[505, 5834])).
% 1.04/1.27 tff(5836,plain,
% 1.04/1.27 (~r(z, elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[3670, 180, 441, 5835])).
% 1.04/1.27 tff(5837,plain,
% 1.04/1.27 (b(z, elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[556, 5836, 109])).
% 1.04/1.27 tff(5838,plain,
% 1.04/1.27 (~r(s(elem!1), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[3593, 158, 270, 797, 156])).
% 1.04/1.27 tff(5839,plain,
% 1.04/1.27 (b(s(elem!1), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[167, 5838, 43])).
% 1.04/1.27 tff(5840,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5841,plain,
% 1.04/1.27 (((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5842,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5841])).
% 1.04/1.27 tff(5843,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5842, 5840])).
% 1.04/1.27 tff(5844,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5845,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5844, 5843])).
% 1.04/1.27 tff(5846,plain,
% 1.04/1.27 (~b(z, s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5845, 206, 5839, 797])).
% 1.04/1.27 tff(5847,plain,
% 1.04/1.27 (r(z, s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[817, 150, 5846, 235])).
% 1.04/1.27 tff(5848,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5849,plain,
% 1.04/1.27 (((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z)))) <=> ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5850,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z)))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5849])).
% 1.04/1.27 tff(5851,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5850, 5848])).
% 1.04/1.27 tff(5852,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5853,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(z, s(z)))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5852, 5851])).
% 1.04/1.27 tff(5854,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5853, 180, 5847, 158, 485])).
% 1.04/1.27 tff(5855,plain,((~r(s(z), s(elem!1))) | (~r(z, s(z))) | (~b(z, elem!1)) | (s(elem!1) = elem!1) | (~r(s(elem!1), z)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(5856,plain,
% 1.04/1.27 (~r(s(z), s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5855, 5837, 156, 43, 5835, 270])).
% 1.04/1.27 tff(5857,plain,
% 1.04/1.27 (b(s(z), s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[467, 5856, 59])).
% 1.04/1.27 tff(5858,plain,
% 1.04/1.27 (~b(s(z), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[4974, 206, 335, 5857])).
% 1.04/1.27 tff(5859,plain,
% 1.04/1.27 (r(s(z), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[193, 5858, 156])).
% 1.04/1.27 tff(5860,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 1.04/1.27 tff(5861,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5862,plain,
% 1.04/1.27 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5863,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5862])).
% 1.04/1.27 tff(5864,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5863, 5861])).
% 1.04/1.27 tff(5865,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5866,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5865, 5864])).
% 1.04/1.27 tff(5867,plain,
% 1.04/1.27 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5866, 180, 5860, 255])).
% 1.04/1.27 tff(5868,plain,
% 1.04/1.27 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[2753, 150, 2750, 5867])).
% 1.04/1.27 tff(5869,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5870,plain,
% 1.04/1.27 (((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5871,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5870])).
% 1.04/1.27 tff(5872,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5871, 5869])).
% 1.04/1.27 tff(5873,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5874,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5873, 5872])).
% 1.04/1.27 tff(5875,plain,
% 1.04/1.27 (~r(s(s(s(s(z)))), s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5874, 180, 169, 5860])).
% 1.04/1.27 tff(5876,plain,
% 1.04/1.27 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5877,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z)))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5878,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(z)) | b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5877, 5876])).
% 1.04/1.27 tff(5879,plain,
% 1.04/1.27 (b(s(s(s(s(z)))), s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5878, 150, 1050, 5875])).
% 1.04/1.27 tff(5880,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5881,plain,
% 1.04/1.27 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5882,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5881])).
% 1.04/1.27 tff(5883,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5882, 5880])).
% 1.04/1.27 tff(5884,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5885,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5884, 5883])).
% 1.04/1.27 tff(5886,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5885, 206, 242, 5879, 5868])).
% 1.04/1.27 tff(5887,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(s(elem!1)), s(z))) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(5888,plain,
% 1.04/1.27 (~r(s(s(s(s(z)))), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5887, 5833, 2750, 5859, 255])).
% 1.04/1.27 tff(5889,plain,
% 1.04/1.27 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5890,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5891,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5890, 5889])).
% 1.04/1.27 tff(5892,plain,
% 1.04/1.27 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5891, 150])).
% 1.04/1.27 tff(5893,plain,
% 1.04/1.27 (b(s(s(s(s(z)))), elem!1)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5892, 5888, 5828])).
% 1.04/1.27 tff(5894,plain,
% 1.04/1.27 (~b(s(s(s(s(z)))), z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[2734, 206, 5837, 5893])).
% 1.04/1.27 tff(5895,plain,
% 1.04/1.27 (r(s(s(s(s(z)))), z)),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[2740, 150, 2737, 5894])).
% 1.04/1.27 tff(5896,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5897,plain,
% 1.04/1.27 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5898,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5897])).
% 1.04/1.27 tff(5899,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5898, 5896])).
% 1.04/1.27 tff(5900,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5901,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5900, 5899])).
% 1.04/1.27 tff(5902,plain,
% 1.04/1.27 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5901, 206, 1168, 5893])).
% 1.04/1.27 tff(5903,plain,
% 1.04/1.27 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5904,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z))))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5905,plain,
% 1.04/1.27 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(z))))) | b(s(elem!1), s(s(s(s(z))))) | r(s(elem!1), s(s(s(s(z)))))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5904, 5903])).
% 1.04/1.27 tff(5906,plain,
% 1.04/1.27 (r(s(elem!1), s(s(s(s(z)))))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5905, 150, 5831, 5902])).
% 1.04/1.27 tff(5907,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5908,plain,
% 1.04/1.27 (((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.04/1.27 inference(rewrite,[status(thm)],[])).
% 1.04/1.27 tff(5909,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.04/1.27 inference(monotonicity,[status(thm)],[5908])).
% 1.04/1.27 tff(5910,plain,
% 1.04/1.27 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.04/1.27 inference(transitivity,[status(thm)],[5909, 5907])).
% 1.04/1.27 tff(5911,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), z)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.04/1.27 inference(quant_inst,[status(thm)],[])).
% 1.04/1.27 tff(5912,plain,
% 1.04/1.27 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.04/1.27 inference(modus_ponens,[status(thm)],[5911, 5910])).
% 1.04/1.27 tff(5913,plain,
% 1.04/1.27 ($false),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5912, 180, 270, 5906, 5895])).
% 1.04/1.27 tff(5914,plain,((~r(elem!1, s(z))) | (~r(s(elem!1), z)) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(z)))) = elem!1) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (s(z) = elem!1) | (~b(elem!1, s(elem!1))) | (s(z) = s(elem!1)) | (s(elem!1) = elem!1) | (z = elem!1) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.27 tff(5915,plain,
% 1.04/1.27 (~r(elem!1, s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[5914, 270, 5831, 5830, 5828, 2750, 255, 156, 335, 244, 43, 240, 5827])).
% 1.04/1.27 tff(5916,plain,
% 1.04/1.27 (b(elem!1, s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[154, 5915, 163])).
% 1.04/1.27 tff(5917,plain,
% 1.04/1.27 (~(elem!1 = s(elem!1))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[45, 43])).
% 1.04/1.27 tff(5918,plain,
% 1.04/1.27 (~b(s(elem!1), s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[4939, 5916, 5830])).
% 1.04/1.27 tff(5919,plain,
% 1.04/1.27 (r(s(elem!1), s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[1652, 5918, 99])).
% 1.04/1.27 tff(5920,plain,
% 1.04/1.27 (~r(z, s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[3782, 5919, 270])).
% 1.04/1.27 tff(5921,plain,
% 1.04/1.27 (b(z, s(z))),
% 1.04/1.27 inference(unit_resolution,[status(thm)],[505, 5920])).
% 1.04/1.27 tff(5922,plain,
% 1.04/1.27 (~b(s(z), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[4885, 5921, 5917, 270, 620, 5916])).
% 1.04/1.28 tff(5923,plain,
% 1.04/1.28 (r(s(z), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[467, 5922, 244])).
% 1.04/1.28 tff(5924,plain,
% 1.04/1.28 (~b(s(s(elem!1)), s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[2363, 5921, 5827])).
% 1.04/1.28 tff(5925,plain,
% 1.04/1.28 (r(s(s(elem!1)), s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[778, 5924])).
% 1.04/1.28 tff(5926,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[858, 5925, 5923, 254])).
% 1.04/1.28 tff(5927,plain,((~r(s(elem!1), z)) | (~r(s(s(elem!1)), s(elem!1))) | (s(elem!1) = s(z)) | (s(elem!1) = s(s(s(s(z))))) | (s(s(s(s(z)))) = elem!1) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(s(elem!1)), elem!1)) | (s(z) = elem!1) | (~b(elem!1, s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(5928,plain,
% 1.04/1.28 (~r(s(elem!1), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5927, 5798, 5782, 5825, 5776, 5813, 254, 5777, 335, 38])).
% 1.04/1.28 tff(5929,plain,
% 1.04/1.28 (b(s(elem!1), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[283, 5928])).
% 1.04/1.28 tff(5930,plain,
% 1.04/1.28 (~b(z, elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[1188, 5929, 5800])).
% 1.04/1.28 tff(5931,plain,
% 1.04/1.28 (r(z, elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[556, 5930, 5801])).
% 1.04/1.28 tff(5932,plain,
% 1.04/1.28 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = s(z))),
% 1.04/1.28 inference(commutativity,[status(thm)],[])).
% 1.04/1.28 tff(5933,plain,
% 1.04/1.28 ((s(s(elem!1)) = s(z)) <=> (s(z) = s(s(elem!1)))),
% 1.04/1.28 inference(symmetry,[status(thm)],[5932])).
% 1.04/1.28 tff(5934,plain,
% 1.04/1.28 ((~(s(s(elem!1)) = s(z))) <=> (~(s(z) = s(s(elem!1))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5933])).
% 1.04/1.28 tff(5935,plain,
% 1.04/1.28 (~(s(z) = s(s(elem!1)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[772, 5934])).
% 1.04/1.28 tff(5936,plain,
% 1.04/1.28 (~b(s(z), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5002, 5931, 38, 5782, 5777, 335, 5929])).
% 1.04/1.28 tff(5937,plain,
% 1.04/1.28 (r(s(z), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[467, 5936, 5783])).
% 1.04/1.28 tff(5938,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5939,plain,
% 1.04/1.28 (((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5940,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5939])).
% 1.04/1.28 tff(5941,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[5940, 5938])).
% 1.04/1.28 tff(5942,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(5943,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5942, 5941])).
% 1.04/1.28 tff(5944,plain,
% 1.04/1.28 (~r(s(z), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5943, 180, 5937, 254])).
% 1.04/1.28 tff(5945,plain,
% 1.04/1.28 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5946,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(5947,plain,
% 1.04/1.28 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5946, 5945])).
% 1.04/1.28 tff(5948,plain,
% 1.04/1.28 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5947, 150, 5944])).
% 1.04/1.28 tff(5949,plain,
% 1.04/1.28 (b(s(z), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5948, 5935])).
% 1.04/1.28 tff(5950,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5951,plain,
% 1.04/1.28 (((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5952,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5951])).
% 1.04/1.28 tff(5953,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.04/1.28 inference(transitivity,[status(thm)],[5952, 5950])).
% 1.04/1.28 tff(5954,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(5955,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5954, 5953])).
% 1.04/1.28 tff(5956,plain,
% 1.04/1.28 (~r(z, s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5955, 180, 5931, 254, 5798])).
% 1.04/1.28 tff(5957,plain,
% 1.04/1.28 (b(z, s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[2185, 5956])).
% 1.04/1.28 tff(5958,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5959,plain,
% 1.04/1.28 (((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(5960,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5959])).
% 1.04/1.28 tff(5961,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[5960, 5958])).
% 1.04/1.28 tff(5962,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(z), z)))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(5963,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[5962, 5961])).
% 1.04/1.28 tff(5964,plain,
% 1.04/1.28 (~b(s(z), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5963, 206, 5957, 5949])).
% 1.04/1.28 tff(5965,plain,
% 1.04/1.28 (r(s(z), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[794, 5964])).
% 1.04/1.28 tff(5966,plain,
% 1.04/1.28 (~r(s(z), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[4984, 5965, 5931])).
% 1.04/1.28 tff(5967,plain,
% 1.04/1.28 (b(s(z), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[193, 5966, 5777])).
% 1.04/1.28 tff(5968,plain,
% 1.04/1.28 (~(s(s(s(s(z)))) = elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5775, 2883])).
% 1.04/1.28 tff(5969,plain,
% 1.04/1.28 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(elem!1))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5809])).
% 1.04/1.28 tff(5970,plain,
% 1.04/1.28 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.04/1.28 inference(symmetry,[status(thm)],[5969])).
% 1.04/1.28 tff(5971,plain,
% 1.04/1.28 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[72, 5970, 1023])).
% 1.04/1.28 tff(5972,plain,
% 1.04/1.28 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5971])).
% 1.04/1.28 tff(5973,plain,
% 1.04/1.28 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.04/1.28 inference(symmetry,[status(thm)],[5972])).
% 1.04/1.28 tff(5974,plain,
% 1.04/1.28 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.28 inference(monotonicity,[status(thm)],[2883])).
% 1.04/1.28 tff(5975,plain,
% 1.04/1.28 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 1.04/1.28 inference(transitivity,[status(thm)],[5974, 5973])).
% 1.04/1.28 tff(5976,plain,
% 1.04/1.28 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.04/1.28 inference(monotonicity,[status(thm)],[2883])).
% 1.04/1.28 tff(5977,plain,
% 1.04/1.28 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[5976, 63])).
% 1.04/1.28 tff(5978,plain,
% 1.04/1.28 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.04/1.28 inference(symmetry,[status(thm)],[5977])).
% 1.04/1.28 tff(5979,plain,
% 1.04/1.28 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5971])).
% 1.04/1.28 tff(5980,plain,
% 1.04/1.28 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[5979, 5978])).
% 1.04/1.28 tff(5981,plain,
% 1.04/1.28 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5980])).
% 1.04/1.28 tff(5982,plain,
% 1.04/1.28 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[24, 5981])).
% 1.04/1.28 tff(5983,plain,
% 1.04/1.28 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), elem!1)),
% 1.04/1.28 inference(monotonicity,[status(thm)],[2883])).
% 1.04/1.28 tff(5984,plain,
% 1.04/1.28 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.28 inference(symmetry,[status(thm)],[5983])).
% 1.04/1.28 tff(5985,plain,
% 1.04/1.28 (b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[1168, 5984])).
% 1.04/1.28 tff(5986,plain,
% 1.04/1.28 (~b(s(s(s(elem!1))), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[365, 95, 5985])).
% 1.04/1.28 tff(5987,plain,
% 1.04/1.28 (r(s(s(s(elem!1))), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[372, 5986])).
% 1.04/1.28 tff(5988,plain,
% 1.04/1.28 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.28 inference(monotonicity,[status(thm)],[5971])).
% 1.04/1.28 tff(5989,plain,
% 1.04/1.28 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(elem!1)), elem!1)),
% 1.04/1.28 inference(symmetry,[status(thm)],[5988])).
% 1.04/1.28 tff(5990,plain,
% 1.04/1.28 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.28 inference(monotonicity,[status(thm)],[2883])).
% 1.04/1.28 tff(5991,plain,
% 1.04/1.28 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), elem!1)),
% 1.04/1.28 inference(transitivity,[status(thm)],[5990, 5989])).
% 1.04/1.28 tff(5992,plain,
% 1.04/1.28 (r(s(s(elem!1)), elem!1)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[2475, 5991])).
% 1.04/1.28 tff(5993,plain,
% 1.04/1.28 (~r(s(s(elem!1)), s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[3694, 5992, 441])).
% 1.04/1.28 tff(5994,plain,
% 1.04/1.28 (b(s(s(elem!1)), s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[778, 5993])).
% 1.04/1.28 tff(5995,plain,
% 1.04/1.28 (r(s(s(s(elem!1))), s(z)) <=> r(elem!1, s(z))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[2883])).
% 1.04/1.28 tff(5996,plain,
% 1.04/1.28 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 1.04/1.28 inference(symmetry,[status(thm)],[5995])).
% 1.04/1.28 tff(5997,plain,
% 1.04/1.28 (r(s(s(s(elem!1))), s(z))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[441, 5996])).
% 1.04/1.28 tff(5998,plain,
% 1.04/1.28 (~r(z, s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[493, 60, 5997])).
% 1.04/1.28 tff(5999,plain,
% 1.04/1.28 (b(z, s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[505, 5998])).
% 1.04/1.28 tff(6000,plain,
% 1.04/1.28 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), elem!1)),
% 1.04/1.28 inference(monotonicity,[status(thm)],[2883])).
% 1.04/1.28 tff(6001,plain,
% 1.04/1.28 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.28 inference(symmetry,[status(thm)],[6000])).
% 1.04/1.28 tff(6002,plain,
% 1.04/1.28 (r(s(s(s(s(s(elem!1))))), s(s(s(elem!1)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[5990, 5989, 6001])).
% 1.04/1.28 tff(6003,plain,
% 1.04/1.28 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[2475, 6002])).
% 1.04/1.28 tff(6004,plain,
% 1.04/1.28 (~r(s(s(elem!1)), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[588, 6003, 60])).
% 1.04/1.28 tff(6005,plain,
% 1.04/1.28 (b(s(s(elem!1)), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[228, 6004])).
% 1.04/1.28 tff(6006,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[2361, 206, 6005, 5999, 5994])).
% 1.04/1.28 tff(6007,plain,((~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))) | (~r(elem!1, s(z))) | (~r(s(s(s(elem!1))), z)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(6008,plain,
% 1.04/1.28 (~r(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[6007, 5987, 441, 2883])).
% 1.04/1.28 tff(6009,plain,
% 1.04/1.28 (b(s(s(s(s(s(elem!1))))), s(s(s(elem!1))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[2431, 6008, 5982])).
% 1.04/1.28 tff(6010,plain,
% 1.04/1.28 (b(s(s(elem!1)), elem!1)),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[6009, 5975])).
% 1.04/1.28 tff(6011,plain,
% 1.04/1.28 (~(s(elem!1) = s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5824, 2883])).
% 1.04/1.28 tff(6012,plain,
% 1.04/1.28 (~(s(s(elem!1)) = s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5812, 2883])).
% 1.04/1.28 tff(6013,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(6014,plain,
% 1.04/1.28 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(6015,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[6014])).
% 1.04/1.28 tff(6016,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[6015, 6013])).
% 1.04/1.28 tff(6017,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(6018,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[6017, 6016])).
% 1.04/1.28 tff(6019,plain,
% 1.04/1.28 (~b(s(s(elem!1)), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[6018, 206, 1168, 95, 6010])).
% 1.04/1.28 tff(6020,plain,
% 1.04/1.28 (r(s(s(elem!1)), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[605, 6019, 57])).
% 1.04/1.28 tff(6021,plain,
% 1.04/1.28 (~b(s(elem!1), s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5901, 206, 1168, 2728])).
% 1.04/1.28 tff(6022,plain,
% 1.04/1.28 (r(s(elem!1), s(s(s(s(z)))))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5905, 150, 5831, 6021])).
% 1.04/1.28 tff(6023,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(6024,plain,
% 1.04/1.28 (((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1)))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(6025,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[6024])).
% 1.04/1.28 tff(6026,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[6025, 6023])).
% 1.04/1.28 tff(6027,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(6028,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[6027, 6026])).
% 1.04/1.28 tff(6029,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[6028, 180, 254, 6022, 2754])).
% 1.04/1.28 tff(6030,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (s(s(elem!1)) = s(s(s(s(z))))) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(6031,plain,
% 1.04/1.28 (~b(s(s(s(s(z)))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[6030, 6020, 6012, 6011, 6010, 1168])).
% 1.04/1.28 tff(6032,plain,
% 1.04/1.28 (r(s(s(s(s(z)))), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5892, 6031, 5968])).
% 1.04/1.28 tff(6033,plain,
% 1.04/1.28 (r(s(s(s(elem!1))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[2883])).
% 1.04/1.28 tff(6034,plain,
% 1.04/1.28 (r(elem!1, s(elem!1)) <=> r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.28 inference(symmetry,[status(thm)],[6033])).
% 1.04/1.28 tff(6035,plain,
% 1.04/1.28 (~b(elem!1, s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5002, 543, 43, 95, 99, 5773, 607])).
% 1.04/1.28 tff(6036,plain,
% 1.04/1.28 (r(elem!1, s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[401, 6035, 5917])).
% 1.04/1.28 tff(6037,plain,
% 1.04/1.28 (r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[6036, 6034])).
% 1.04/1.28 tff(6038,plain,
% 1.04/1.28 (~r(s(z), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[436, 304, 243])).
% 1.04/1.28 tff(6039,plain,
% 1.04/1.28 (b(s(z), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[467, 6038, 59])).
% 1.04/1.28 tff(6040,plain,
% 1.04/1.28 (~b(z, s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[951, 6039, 911])).
% 1.04/1.28 tff(6041,plain,
% 1.04/1.28 (r(elem!1, s(elem!1))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[304, 6033])).
% 1.04/1.28 tff(6042,plain,
% 1.04/1.28 (~r(z, s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[939, 6041, 543])).
% 1.04/1.28 tff(6043,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[817, 150, 6042, 6040, 235])).
% 1.04/1.28 tff(6044,plain,((~r(s(s(s(elem!1))), s(elem!1))) | (~r(z, elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(z, s(z))) | (s(z) = s(elem!1)) | (~r(s(s(s(elem!1))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(6045,plain,
% 1.04/1.28 (~b(z, s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[6044, 6037, 2883, 543, 244, 5997])).
% 1.04/1.28 tff(6046,plain,
% 1.04/1.28 (r(z, s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[505, 6045])).
% 1.04/1.28 tff(6047,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(6048,plain,
% 1.04/1.28 (((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.04/1.28 inference(rewrite,[status(thm)],[])).
% 1.04/1.28 tff(6049,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(elem!1, s(z)))))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[6048])).
% 1.04/1.28 tff(6050,plain,
% 1.04/1.28 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 1.04/1.28 inference(transitivity,[status(thm)],[6049, 6047])).
% 1.04/1.28 tff(6051,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(elem!1, s(elem!1))) | (~r(z, elem!1)))),
% 1.04/1.28 inference(quant_inst,[status(thm)],[])).
% 1.04/1.28 tff(6052,plain,
% 1.04/1.28 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(elem!1))) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[6051, 6050])).
% 1.04/1.28 tff(6053,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[6052, 180, 6036, 543, 441, 6046])).
% 1.04/1.28 tff(6054,plain,((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~(s(s(s(elem!1))) = elem!1)) | (s(elem!1) = elem!1) | (~b(s(elem!1), z)) | (s(elem!1) = s(z)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(6055,plain,
% 1.04/1.28 (~b(s(z), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[6054, 2305, 2883, 38, 95, 1228, 441])).
% 1.04/1.28 tff(6056,plain,
% 1.04/1.28 (r(s(z), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[467, 6055, 1229])).
% 1.04/1.28 tff(6057,plain,
% 1.04/1.28 (~r(s(z), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5943, 180, 6056, 6020])).
% 1.04/1.28 tff(6058,plain,
% 1.04/1.28 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[5947, 150, 6057])).
% 1.04/1.28 tff(6059,plain,
% 1.04/1.28 (b(s(z), s(s(elem!1)))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[6058, 5935])).
% 1.04/1.28 tff(6060,plain,
% 1.04/1.28 (~r(z, s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[493, 5987, 5997])).
% 1.04/1.28 tff(6061,plain,
% 1.04/1.28 (b(z, s(z))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[505, 6060])).
% 1.04/1.28 tff(6062,plain,
% 1.04/1.28 (~r(s(z), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[858, 4817, 898])).
% 1.04/1.28 tff(6063,plain,
% 1.04/1.28 (b(s(z), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[467, 6062, 1229])).
% 1.04/1.28 tff(6064,plain,
% 1.04/1.28 (~b(z, elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[3920, 196, 441, 911, 24])).
% 1.04/1.28 tff(6065,plain,
% 1.04/1.28 (r(z, elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[556, 6064, 109])).
% 1.04/1.28 tff(6066,plain,
% 1.04/1.28 (b(s(s(s(elem!1))), s(elem!1)) <=> b(elem!1, s(elem!1))),
% 1.04/1.28 inference(monotonicity,[status(thm)],[2883])).
% 1.04/1.28 tff(6067,plain,
% 1.04/1.28 (~r(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[6044, 6065, 2883, 911, 1229, 5997])).
% 1.04/1.28 tff(6068,plain,
% 1.04/1.28 (b(s(s(s(elem!1))), s(elem!1))),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[293, 6067, 11])).
% 1.04/1.28 tff(6069,plain,
% 1.04/1.28 (b(elem!1, s(elem!1))),
% 1.04/1.28 inference(modus_ponens,[status(thm)],[6068, 6066])).
% 1.04/1.28 tff(6070,plain,
% 1.04/1.28 (~b(s(z), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[4974, 206, 6069, 6063])).
% 1.04/1.28 tff(6071,plain,
% 1.04/1.28 (r(s(z), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[193, 6070, 5773])).
% 1.04/1.28 tff(6072,plain,
% 1.04/1.28 (~r(s(z), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[4984, 6071, 6065])).
% 1.04/1.28 tff(6073,plain,
% 1.04/1.28 (b(s(z), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[794, 6072])).
% 1.04/1.28 tff(6074,plain,
% 1.04/1.28 (~r(s(elem!1), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[4998, 6071, 1228, 95, 6065])).
% 1.04/1.28 tff(6075,plain,
% 1.04/1.28 (b(s(elem!1), elem!1)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[167, 6074, 38])).
% 1.04/1.28 tff(6076,plain,
% 1.04/1.28 ($false),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[4623, 206, 6075, 95, 6073, 6063])).
% 1.04/1.28 tff(6077,plain,((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(z, s(z))) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (z = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.28 tff(6078,plain,
% 1.04/1.28 (~b(s(s(elem!1)), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[6077, 6061, 95, 2883, 11, 109, 441])).
% 1.04/1.28 tff(6079,plain,
% 1.04/1.28 (r(s(s(elem!1)), z)),
% 1.04/1.28 inference(unit_resolution,[status(thm)],[228, 6078])).
% 1.04/1.28 tff(6080,plain,
% 1.04/1.29 (r(s(s(s(elem!1))), z) <=> r(elem!1, z)),
% 1.04/1.29 inference(monotonicity,[status(thm)],[2883])).
% 1.04/1.29 tff(6081,plain,
% 1.04/1.29 (r(elem!1, z)),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[5987, 6080])).
% 1.04/1.29 tff(6082,plain,
% 1.04/1.29 (~r(elem!1, s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[4612, 180, 6081, 6079])).
% 1.04/1.29 tff(6083,plain,
% 1.04/1.29 (b(elem!1, s(s(elem!1)))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[889, 6082, 24])).
% 1.04/1.29 tff(6084,plain,
% 1.04/1.29 (~r(elem!1, s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[450, 6056, 441])).
% 1.04/1.29 tff(6085,plain,
% 1.04/1.29 (b(elem!1, s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[401, 6084, 46])).
% 1.04/1.29 tff(6086,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6087,plain,
% 1.04/1.29 (((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1))) <=> ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6088,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6087])).
% 1.04/1.29 tff(6089,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[6088, 6086])).
% 1.04/1.29 tff(6090,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(elem!1, s(elem!1))) | (~b(s(z), elem!1)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(6091,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[6090, 6089])).
% 1.04/1.29 tff(6092,plain,
% 1.04/1.29 (~b(s(z), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6091, 206, 6085, 6083, 6059])).
% 1.04/1.29 tff(6093,plain,
% 1.04/1.29 (r(s(z), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[193, 6092, 5773])).
% 1.04/1.29 tff(6094,plain,
% 1.04/1.29 (~r(s(s(s(s(z)))), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[5874, 180, 6093, 6032])).
% 1.04/1.29 tff(6095,plain,
% 1.04/1.29 (b(s(s(s(s(z)))), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[5878, 150, 1050, 6094])).
% 1.04/1.29 tff(6096,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6097,plain,
% 1.04/1.29 (((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6098,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6097])).
% 1.04/1.29 tff(6099,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.04/1.29 inference(transitivity,[status(thm)],[6098, 6096])).
% 1.04/1.29 tff(6100,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(6101,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[6100, 6099])).
% 1.04/1.29 tff(6102,plain,
% 1.04/1.29 (~r(s(s(s(s(z)))), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6101, 180, 2305, 6032])).
% 1.04/1.29 tff(6103,plain,
% 1.04/1.29 (b(s(s(s(s(z)))), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[2740, 150, 2737, 6102])).
% 1.04/1.29 tff(6104,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6105,plain,
% 1.04/1.29 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6106,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6105])).
% 1.04/1.29 tff(6107,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[6106, 6104])).
% 1.04/1.29 tff(6108,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(6109,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[6108, 6107])).
% 1.04/1.29 tff(6110,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6109, 206, 6061, 6103, 6095])).
% 1.04/1.29 tff(6111,plain,((~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(s(elem!1))) = s(elem!1)) | (z = elem!1) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(6112,plain,
% 1.04/1.29 (~r(elem!1, s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6111, 5929, 5757, 11, 5801, 5800])).
% 1.04/1.29 tff(6113,plain,
% 1.04/1.29 (b(elem!1, s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[154, 6112, 5778])).
% 1.04/1.29 tff(6114,plain,
% 1.04/1.29 (~b(s(elem!1), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[4939, 6113, 5800])).
% 1.04/1.29 tff(6115,plain,
% 1.04/1.29 (r(s(elem!1), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1652, 6114, 5782])).
% 1.04/1.29 tff(6116,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6117,plain,
% 1.04/1.29 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6118,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6117])).
% 1.04/1.29 tff(6119,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.04/1.29 inference(transitivity,[status(thm)],[6118, 6116])).
% 1.04/1.29 tff(6120,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(6121,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[6120, 6119])).
% 1.04/1.29 tff(6122,plain,
% 1.04/1.29 (~b(s(s(s(s(z)))), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6121, 206, 117, 2728])).
% 1.04/1.29 tff(6123,plain,
% 1.04/1.29 (r(s(s(s(s(z)))), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[5878, 150, 1050, 6122])).
% 1.04/1.29 tff(6124,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6125,plain,
% 1.04/1.29 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6126,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6125])).
% 1.04/1.29 tff(6127,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[6126, 6124])).
% 1.04/1.29 tff(6128,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(6129,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[6128, 6127])).
% 1.04/1.29 tff(6130,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6129, 180, 3774, 6123, 6022])).
% 1.04/1.29 tff(6131,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(z))) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(6132,plain,
% 1.04/1.29 (~b(s(s(s(s(z)))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6131, 6115, 5825, 5967, 5800])).
% 1.04/1.29 tff(6133,plain,
% 1.04/1.29 (r(s(s(s(s(z)))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[5892, 6132, 5776])).
% 1.04/1.29 tff(6134,plain,
% 1.04/1.29 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[5866, 180, 6133, 5798])).
% 1.04/1.29 tff(6135,plain,
% 1.04/1.29 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[2753, 150, 5813, 6134])).
% 1.04/1.29 tff(6136,plain,
% 1.04/1.29 (~r(s(s(s(s(z)))), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6101, 180, 5931, 6133])).
% 1.04/1.29 tff(6137,plain,
% 1.04/1.29 (b(s(s(s(s(z)))), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[2740, 150, 2737, 6136])).
% 1.04/1.29 tff(6138,plain,
% 1.04/1.29 (r(s(s(elem!1)), s(s(s(elem!1)))) <=> r(s(s(elem!1)), elem!1)),
% 1.04/1.29 inference(monotonicity,[status(thm)],[5757])).
% 1.04/1.29 tff(6139,plain,
% 1.04/1.29 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.29 inference(symmetry,[status(thm)],[6138])).
% 1.04/1.29 tff(6140,plain,
% 1.04/1.29 (r(s(s(s(s(s(elem!1))))), elem!1) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[5797, 6139])).
% 1.04/1.29 tff(6141,plain,
% 1.04/1.29 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[2948, 6140])).
% 1.04/1.29 tff(6142,plain,
% 1.04/1.29 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(elem!1), elem!1)),
% 1.04/1.29 inference(monotonicity,[status(thm)],[5757])).
% 1.04/1.29 tff(6143,plain,
% 1.04/1.29 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.29 inference(symmetry,[status(thm)],[6142])).
% 1.04/1.29 tff(6144,plain,
% 1.04/1.29 (b(s(elem!1), s(s(s(elem!1))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[5800, 6143])).
% 1.04/1.29 tff(6145,plain,
% 1.04/1.29 (~b(s(s(s(elem!1))), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[365, 5929, 6144])).
% 1.04/1.29 tff(6146,plain,
% 1.04/1.29 (r(s(s(s(elem!1))), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[372, 6145])).
% 1.04/1.29 tff(6147,plain,
% 1.04/1.29 (~r(s(s(elem!1)), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[588, 6146, 6141])).
% 1.04/1.29 tff(6148,plain,
% 1.04/1.29 (b(s(s(elem!1)), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[228, 6147])).
% 1.04/1.29 tff(6149,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6150,plain,
% 1.04/1.29 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6151,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6150])).
% 1.04/1.29 tff(6152,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[6151, 6149])).
% 1.04/1.29 tff(6153,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(6154,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[6153, 6152])).
% 1.04/1.29 tff(6155,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6154, 206, 6148, 6137, 6135])).
% 1.04/1.29 tff(6156,plain,((~r(s(s(s(s(s(elem!1))))), elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(6157,plain,
% 1.04/1.29 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6156, 5793, 254, 11])).
% 1.04/1.29 tff(6158,plain,
% 1.04/1.29 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[2377, 6157, 5791])).
% 1.04/1.29 tff(6159,plain,
% 1.04/1.29 (b(s(s(elem!1)), s(s(s(elem!1)))) <=> b(s(s(elem!1)), elem!1)),
% 1.04/1.29 inference(monotonicity,[status(thm)],[2883])).
% 1.04/1.29 tff(6160,plain,
% 1.04/1.29 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.29 inference(symmetry,[status(thm)],[6159])).
% 1.04/1.29 tff(6161,plain,
% 1.04/1.29 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.04/1.29 inference(transitivity,[status(thm)],[1096, 5969, 71])).
% 1.04/1.29 tff(6162,plain,
% 1.04/1.29 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6161])).
% 1.04/1.29 tff(6163,plain,
% 1.04/1.29 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[6162, 6160])).
% 1.04/1.29 tff(6164,plain,
% 1.04/1.29 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[3363, 6163])).
% 1.04/1.29 tff(6165,assumption,(~b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 1.04/1.29 tff(6166,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6165, 6164])).
% 1.04/1.29 tff(6167,plain,((~b(s(s(s(s(s(elem!1))))), elem!1)) | b(s(s(elem!1)), s(s(s(elem!1)))) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(6168,plain,
% 1.04/1.29 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6167, 6158, 5757])).
% 1.04/1.29 tff(6169,plain,
% 1.04/1.29 (~b(s(z), s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[907, 735, 61])).
% 1.04/1.29 tff(6170,plain,
% 1.04/1.29 (r(s(z), s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[467, 6169, 59])).
% 1.04/1.29 tff(6171,plain,
% 1.04/1.29 (~b(s(s(elem!1)), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[759, 735, 751])).
% 1.04/1.29 tff(6172,plain,
% 1.04/1.29 (r(s(s(elem!1)), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[778, 6171])).
% 1.04/1.29 tff(6173,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[858, 6172, 6170, 254])).
% 1.04/1.29 tff(6174,plain,((~b(s(s(s(elem!1))), s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (s(z) = s(elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(elem!1))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(6175,plain,
% 1.04/1.29 (~b(s(s(s(elem!1))), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6174, 6168, 5783, 254, 61])).
% 1.04/1.29 tff(6176,plain,
% 1.04/1.29 (~b(elem!1, s(z))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[6175, 5780])).
% 1.04/1.29 tff(6177,plain,
% 1.04/1.29 (r(elem!1, s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[154, 6176, 5778])).
% 1.04/1.29 tff(6178,plain,
% 1.04/1.29 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.04/1.29 inference(transitivity,[status(thm)],[5784, 5757])).
% 1.04/1.29 tff(6179,plain,
% 1.04/1.29 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(elem!1, s(z))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6178])).
% 1.04/1.29 tff(6180,plain,
% 1.04/1.29 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.29 inference(symmetry,[status(thm)],[6179])).
% 1.04/1.29 tff(6181,plain,
% 1.04/1.29 (b(s(s(s(elem!1))), s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.29 inference(transitivity,[status(thm)],[5779, 6180])).
% 1.04/1.29 tff(6182,plain,
% 1.04/1.29 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(s(s(s(s(s(s(elem!1)))))), s(z)))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6181])).
% 1.04/1.29 tff(6183,plain,
% 1.04/1.29 (~b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[6175, 6182])).
% 1.04/1.29 tff(6184,plain,
% 1.04/1.29 (r(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[1402, 6183])).
% 1.04/1.29 tff(6185,plain,
% 1.04/1.29 ((elem!1 = s(s(s(s(s(elem!1)))))) <=> (elem!1 = s(s(elem!1)))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6161])).
% 1.04/1.29 tff(6186,plain,
% 1.04/1.29 ((elem!1 = s(s(elem!1))) <=> (elem!1 = s(s(s(s(s(elem!1))))))),
% 1.04/1.29 inference(symmetry,[status(thm)],[6185])).
% 1.04/1.29 tff(6187,plain,
% 1.04/1.29 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.04/1.29 inference(transitivity,[status(thm)],[6186, 64])).
% 1.04/1.29 tff(6188,plain,
% 1.04/1.29 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6187])).
% 1.04/1.29 tff(6189,plain,
% 1.04/1.29 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[517, 6188])).
% 1.04/1.29 tff(6190,assumption,(~r(s(s(s(s(s(elem!1))))), elem!1)), introduced(assumption)).
% 1.04/1.29 tff(6191,plain,
% 1.04/1.29 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[2377, 6190, 6189])).
% 1.04/1.29 tff(6192,plain,
% 1.04/1.29 (b(s(s(elem!1)), elem!1)),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[6191, 6162])).
% 1.04/1.29 tff(6193,plain,
% 1.04/1.29 (~(s(elem!1) = s(z))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[2881, 5808])).
% 1.04/1.29 tff(6194,plain,
% 1.04/1.29 (~(z = elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[239, 6193])).
% 1.04/1.29 tff(6195,plain,
% 1.04/1.29 (~(elem!1 = z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[287, 6194])).
% 1.04/1.29 tff(6196,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6197,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.04/1.29 inference(quant_inst,[status(thm)],[])).
% 1.04/1.29 tff(6198,plain,
% 1.04/1.29 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[6197, 6196])).
% 1.04/1.29 tff(6199,plain,
% 1.04/1.29 ($false),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6198, 206, 335, 652, 2742, 5827])).
% 1.04/1.29 tff(6200,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (elem!1 = z) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.04/1.29 tff(6201,plain,
% 1.04/1.29 (~r(s(elem!1), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6200, 270, 6192, 6195, 335, 254])).
% 1.04/1.29 tff(6202,plain,
% 1.04/1.29 (b(s(elem!1), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[167, 6201, 518])).
% 1.04/1.29 tff(6203,plain,
% 1.04/1.29 (~b(s(s(s(s(z)))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6030, 6202, 6012, 254, 6011, 6192])).
% 1.04/1.29 tff(6204,plain,
% 1.04/1.29 (r(s(s(s(s(z)))), elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[5892, 6203, 5968])).
% 1.04/1.29 tff(6205,plain,
% 1.04/1.29 (~b(z, elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[3706, 5827, 6192])).
% 1.04/1.29 tff(6206,plain,
% 1.04/1.29 (r(z, elem!1)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[556, 6205, 6194])).
% 1.04/1.29 tff(6207,plain,
% 1.04/1.29 (~r(s(s(s(s(z)))), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[6101, 180, 6206, 6204])).
% 1.04/1.29 tff(6208,plain,
% 1.04/1.29 (b(s(s(s(s(z)))), z)),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[2740, 150, 2737, 6207])).
% 1.04/1.29 tff(6209,plain,
% 1.04/1.29 (~(s(z) = s(elem!1))),
% 1.04/1.29 inference(unit_resolution,[status(thm)],[101, 6193])).
% 1.04/1.29 tff(6210,plain,
% 1.04/1.29 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.04/1.29 inference(transitivity,[status(thm)],[5809, 2883])).
% 1.04/1.29 tff(6211,plain,
% 1.04/1.29 (r(s(s(s(s(s(s(elem!1)))))), z) <=> r(elem!1, z)),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6210])).
% 1.04/1.29 tff(6212,plain,
% 1.04/1.29 (r(elem!1, z) <=> r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.04/1.29 inference(symmetry,[status(thm)],[6211])).
% 1.04/1.29 tff(6213,plain,
% 1.04/1.29 ((elem!1 = s(s(elem!1))) <=> (s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[6186, 5978])).
% 1.04/1.29 tff(6214,plain,
% 1.04/1.29 ((~(elem!1 = s(s(elem!1)))) <=> (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6213])).
% 1.04/1.29 tff(6215,plain,
% 1.04/1.29 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[517, 6214])).
% 1.04/1.29 tff(6216,plain,
% 1.04/1.29 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6210])).
% 1.04/1.29 tff(6217,plain,
% 1.04/1.29 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.29 inference(symmetry,[status(thm)],[6216])).
% 1.04/1.29 tff(6218,plain,
% 1.04/1.29 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(elem!1)))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6161])).
% 1.04/1.29 tff(6219,plain,
% 1.04/1.29 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.04/1.29 inference(symmetry,[status(thm)],[6218])).
% 1.04/1.29 tff(6220,plain,
% 1.04/1.29 (r(elem!1, s(s(elem!1))) <=> r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.04/1.29 inference(transitivity,[status(thm)],[6219, 6217])).
% 1.04/1.29 tff(6221,plain,
% 1.04/1.29 ((~r(elem!1, s(s(elem!1)))) <=> (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6220])).
% 1.04/1.29 tff(6222,plain,
% 1.04/1.29 ((elem!1 = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = elem!1)),
% 1.04/1.29 inference(commutativity,[status(thm)],[])).
% 1.04/1.29 tff(6223,plain,
% 1.04/1.29 ((s(s(s(s(z)))) = elem!1) <=> (elem!1 = s(s(s(s(z)))))),
% 1.04/1.29 inference(symmetry,[status(thm)],[6222])).
% 1.04/1.29 tff(6224,plain,
% 1.04/1.29 ((~(s(s(s(s(z)))) = elem!1)) <=> (~(elem!1 = s(s(s(s(z))))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6223])).
% 1.04/1.29 tff(6225,plain,
% 1.04/1.29 (~(elem!1 = s(s(s(s(z)))))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[5968, 6224])).
% 1.04/1.29 tff(6226,plain,
% 1.04/1.29 ((s(s(s(s(z)))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(z)))))),
% 1.04/1.29 inference(commutativity,[status(thm)],[])).
% 1.04/1.29 tff(6227,plain,
% 1.04/1.29 ((s(elem!1) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(elem!1))),
% 1.04/1.29 inference(symmetry,[status(thm)],[6226])).
% 1.04/1.29 tff(6228,plain,
% 1.04/1.29 ((~(s(elem!1) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(elem!1)))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6227])).
% 1.04/1.29 tff(6229,plain,
% 1.04/1.29 (~(s(s(s(s(z)))) = s(elem!1))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[6011, 6228])).
% 1.04/1.29 tff(6230,plain,
% 1.04/1.29 ((s(s(s(s(z)))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(z)))))),
% 1.04/1.29 inference(commutativity,[status(thm)],[])).
% 1.04/1.29 tff(6231,plain,
% 1.04/1.29 ((s(s(elem!1)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(elem!1)))),
% 1.04/1.29 inference(symmetry,[status(thm)],[6230])).
% 1.04/1.29 tff(6232,plain,
% 1.04/1.29 ((~(s(s(elem!1)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(elem!1))))),
% 1.04/1.29 inference(monotonicity,[status(thm)],[6231])).
% 1.04/1.29 tff(6233,plain,
% 1.04/1.29 (~(s(s(s(s(z)))) = s(s(elem!1)))),
% 1.04/1.29 inference(modus_ponens,[status(thm)],[6012, 6232])).
% 1.04/1.29 tff(6234,plain,
% 1.04/1.29 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.04/1.29 inference(rewrite,[status(thm)],[])).
% 1.04/1.29 tff(6235,plain,
% 1.04/1.29 (((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.04/1.30 inference(rewrite,[status(thm)],[])).
% 1.04/1.30 tff(6236,plain,
% 1.04/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.04/1.30 inference(monotonicity,[status(thm)],[6235])).
% 1.04/1.30 tff(6237,plain,
% 1.04/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.04/1.30 inference(transitivity,[status(thm)],[6236, 6234])).
% 1.04/1.30 tff(6238,plain,
% 1.04/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.04/1.30 inference(quant_inst,[status(thm)],[])).
% 1.04/1.30 tff(6239,plain,
% 1.04/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(s(elem!1))))),
% 1.04/1.30 inference(modus_ponens,[status(thm)],[6238, 6237])).
% 1.04/1.30 tff(6240,plain,
% 1.04/1.30 (~b(s(s(s(s(z)))), s(s(elem!1)))),
% 1.04/1.30 inference(unit_resolution,[status(thm)],[6239, 206, 6192, 5827, 6208])).
% 1.04/1.30 tff(6241,plain,
% 1.04/1.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.04/1.30 inference(rewrite,[status(thm)],[])).
% 1.04/1.30 tff(6242,plain,
% 1.04/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.04/1.30 inference(quant_inst,[status(thm)],[])).
% 1.04/1.30 tff(6243,plain,
% 1.04/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(elem!1))) | b(s(s(s(s(z)))), s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.04/1.30 inference(modus_ponens,[status(thm)],[6242, 6241])).
% 1.04/1.30 tff(6244,plain,
% 1.04/1.30 ((s(s(s(s(z)))) = s(s(elem!1))) | r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.04/1.30 inference(unit_resolution,[status(thm)],[6243, 150, 6240])).
% 1.04/1.30 tff(6245,plain,
% 1.04/1.30 (r(s(s(s(s(z)))), s(s(elem!1)))),
% 1.04/1.30 inference(unit_resolution,[status(thm)],[6244, 6233])).
% 1.14/1.30 tff(6246,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6247,plain,
% 1.14/1.30 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6248,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[6247])).
% 1.14/1.30 tff(6249,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[6248, 6246])).
% 1.14/1.30 tff(6250,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(6251,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6250, 6249])).
% 1.14/1.30 tff(6252,plain,
% 1.14/1.30 (~b(s(elem!1), s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6251, 206, 6202, 6192, 5827])).
% 1.14/1.30 tff(6253,plain,
% 1.14/1.30 (r(s(elem!1), s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[692, 6252, 681])).
% 1.14/1.30 tff(6254,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6255,plain,
% 1.14/1.30 (((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6256,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[6255])).
% 1.14/1.30 tff(6257,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1)))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[6256, 6254])).
% 1.14/1.30 tff(6258,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(6259,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(s(s(z)))), s(elem!1))) | (~r(s(s(s(s(z)))), s(s(elem!1))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6258, 6257])).
% 1.14/1.30 tff(6260,plain,
% 1.14/1.30 (~r(s(s(s(s(z)))), s(elem!1))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6259, 180, 270, 6253, 6245])).
% 1.14/1.30 tff(6261,plain,
% 1.14/1.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6262,plain,
% 1.14/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1)))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(6263,plain,
% 1.14/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1)) | r(s(s(s(s(z)))), s(elem!1))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6262, 6261])).
% 1.14/1.30 tff(6264,plain,
% 1.14/1.30 ((s(s(s(s(z)))) = s(elem!1)) | b(s(s(s(s(z)))), s(elem!1))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6263, 150, 6260])).
% 1.14/1.30 tff(6265,plain,
% 1.14/1.30 (b(s(s(s(s(z)))), s(elem!1))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6264, 6229])).
% 1.14/1.30 tff(6266,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6267,plain,
% 1.14/1.30 (((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6268,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[6267])).
% 1.14/1.30 tff(6269,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[6268, 6266])).
% 1.14/1.30 tff(6270,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(6271,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(z)))), s(elem!1))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6270, 6269])).
% 1.14/1.30 tff(6272,plain,
% 1.14/1.30 (~b(elem!1, s(s(s(s(z)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6271, 206, 335, 6265])).
% 1.14/1.30 tff(6273,plain,
% 1.14/1.30 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6274,plain,
% 1.14/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z))))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(6275,plain,
% 1.14/1.30 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6274, 6273])).
% 1.14/1.30 tff(6276,plain,
% 1.14/1.30 ((elem!1 = s(s(s(s(z))))) | r(elem!1, s(s(s(s(z)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6275, 150, 6272])).
% 1.14/1.30 tff(6277,plain,
% 1.14/1.30 (r(elem!1, s(s(s(s(z)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6276, 6225])).
% 1.14/1.30 tff(6278,plain,
% 1.14/1.30 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6154, 206, 5827, 6208])).
% 1.14/1.30 tff(6279,plain,
% 1.14/1.30 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[2753, 150, 6012, 6278])).
% 1.14/1.30 tff(6280,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6281,plain,
% 1.14/1.30 (((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6282,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[6281])).
% 1.14/1.30 tff(6283,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[6282, 6280])).
% 1.14/1.30 tff(6284,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(z)))))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(6285,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(s(s(s(z)))))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6284, 6283])).
% 1.14/1.30 tff(6286,plain,
% 1.14/1.30 (~r(elem!1, s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6285, 180, 254, 6279, 6277])).
% 1.14/1.30 tff(6287,plain,
% 1.14/1.30 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6286, 6221])).
% 1.14/1.30 tff(6288,plain,
% 1.14/1.30 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.14/1.30 inference(symmetry,[status(thm)],[2885])).
% 1.14/1.30 tff(6289,plain,
% 1.14/1.30 (b(elem!1, s(s(elem!1))) <=> b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[6288])).
% 1.14/1.30 tff(6290,plain,
% 1.14/1.30 (b(elem!1, s(s(s(s(s(elem!1)))))) <=> b(elem!1, s(s(elem!1)))),
% 1.14/1.30 inference(symmetry,[status(thm)],[6289])).
% 1.14/1.30 tff(6291,plain,
% 1.14/1.30 ((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[5977])).
% 1.14/1.30 tff(6292,plain,
% 1.14/1.30 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[2979, 6291])).
% 1.14/1.30 tff(6293,plain,
% 1.14/1.30 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[2887])).
% 1.14/1.30 tff(6294,plain,
% 1.14/1.30 ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))) <=> (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[6293])).
% 1.14/1.30 tff(6295,assumption,(~r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.30 tff(6296,plain,
% 1.14/1.30 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6295, 6294])).
% 1.14/1.30 tff(6297,plain,
% 1.14/1.30 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[3488, 6296, 6292])).
% 1.14/1.30 tff(6298,plain,
% 1.14/1.30 (b(elem!1, s(s(elem!1)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6297, 6290])).
% 1.14/1.30 tff(6299,plain,
% 1.14/1.30 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.30 inference(monotonicity,[status(thm)],[6288])).
% 1.14/1.30 tff(6300,plain,
% 1.14/1.30 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.14/1.30 inference(symmetry,[status(thm)],[6299])).
% 1.14/1.30 tff(6301,plain,
% 1.14/1.30 ((s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(elem!1))))) = elem!1)),
% 1.14/1.30 inference(transitivity,[status(thm)],[5977, 64])).
% 1.14/1.30 tff(6302,plain,
% 1.14/1.30 ((~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(elem!1))))) = elem!1))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[6301])).
% 1.14/1.30 tff(6303,plain,
% 1.14/1.30 (~(s(s(s(s(s(elem!1))))) = elem!1)),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[2979, 6302])).
% 1.14/1.30 tff(6304,plain,
% 1.14/1.30 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[2377, 6303, 6190])).
% 1.14/1.30 tff(6305,plain,
% 1.14/1.30 (b(s(s(elem!1)), elem!1)),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6304, 6300])).
% 1.14/1.30 tff(6306,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6307,plain,
% 1.14/1.30 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6308,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[6307])).
% 1.14/1.30 tff(6309,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[6308, 6306])).
% 1.14/1.30 tff(6310,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(6311,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6310, 6309])).
% 1.14/1.30 tff(6312,plain,
% 1.14/1.30 (~b(s(elem!1), s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6311, 206, 1168, 6305])).
% 1.14/1.30 tff(6313,plain,
% 1.14/1.30 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 1.14/1.30 inference(symmetry,[status(thm)],[676])).
% 1.14/1.30 tff(6314,plain,
% 1.14/1.30 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(elem!1) = s(s(elem!1))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[6313])).
% 1.14/1.30 tff(6315,plain,
% 1.14/1.30 ((s(elem!1) = s(s(s(elem!1)))) <=> (s(elem!1) = elem!1)),
% 1.14/1.30 inference(monotonicity,[status(thm)],[2883])).
% 1.14/1.30 tff(6316,plain,
% 1.14/1.30 ((s(elem!1) = s(s(s(elem!1)))) <=> (elem!1 = s(elem!1))),
% 1.14/1.30 inference(transitivity,[status(thm)],[6315, 39])).
% 1.14/1.30 tff(6317,plain,
% 1.14/1.30 ((~(s(elem!1) = s(s(s(elem!1))))) <=> (~(elem!1 = s(elem!1)))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[6316])).
% 1.14/1.30 tff(6318,plain,
% 1.14/1.30 (~(elem!1 = s(elem!1))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[21, 6317])).
% 1.14/1.30 tff(6319,plain,
% 1.14/1.30 (~(s(s(elem!1)) = s(elem!1))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[56, 6318])).
% 1.14/1.30 tff(6320,plain,
% 1.14/1.30 (~(s(elem!1) = s(s(elem!1)))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6319, 6314])).
% 1.14/1.30 tff(6321,plain,
% 1.14/1.30 (r(s(elem!1), s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[692, 6320, 6312])).
% 1.14/1.30 tff(6322,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.14/1.30 tff(6323,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6324,plain,
% 1.14/1.30 (((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z))) <=> ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(rewrite,[status(thm)],[])).
% 1.14/1.30 tff(6325,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.14/1.30 inference(monotonicity,[status(thm)],[6324])).
% 1.14/1.30 tff(6326,plain,
% 1.14/1.30 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.30 inference(transitivity,[status(thm)],[6325, 6323])).
% 1.14/1.30 tff(6327,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)))),
% 1.14/1.30 inference(quant_inst,[status(thm)],[])).
% 1.14/1.30 tff(6328,plain,
% 1.14/1.30 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(z, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.14/1.30 inference(modus_ponens,[status(thm)],[6327, 6326])).
% 1.14/1.30 tff(6329,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6328, 180, 270, 3170, 6322])).
% 1.14/1.30 tff(6330,plain,((~r(z, s(s(elem!1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.30 tff(6331,plain,
% 1.14/1.30 (~r(z, s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6330, 6321, 270])).
% 1.14/1.30 tff(6332,plain,
% 1.14/1.30 (b(z, s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[2185, 6331])).
% 1.14/1.30 tff(6333,plain,
% 1.14/1.30 (~b(elem!1, s(s(elem!1)))),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[3300, 206, 653, 6332])).
% 1.14/1.30 tff(6334,plain,
% 1.14/1.30 ($false),
% 1.14/1.30 inference(unit_resolution,[status(thm)],[6333, 6298])).
% 1.14/1.30 tff(6335,plain,((~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | r(s(s(s(s(s(elem!1))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) | (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(6336,plain,
% 1.14/1.31 (~b(elem!1, z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6335, 6287, 2883, 6190, 270, 6202, 6215, 21])).
% 1.14/1.31 tff(6337,plain,
% 1.14/1.31 (r(elem!1, z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[387, 6336, 6195])).
% 1.14/1.31 tff(6338,plain,
% 1.14/1.31 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[6337, 6212])).
% 1.14/1.31 tff(6339,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1604, 180, 1405, 485, 1564])).
% 1.14/1.31 tff(6340,plain,((~r(z, s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~r(s(s(s(s(s(s(elem!1)))))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(6341,plain,
% 1.14/1.31 (~r(z, s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6340, 6338, 1405])).
% 1.14/1.31 tff(6342,plain,
% 1.14/1.31 (b(z, s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[505, 6341])).
% 1.14/1.31 tff(6343,plain,
% 1.14/1.31 (~b(s(s(elem!1)), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2363, 6342, 5827])).
% 1.14/1.31 tff(6344,plain,
% 1.14/1.31 (r(s(s(elem!1)), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[778, 6343])).
% 1.14/1.31 tff(6345,plain,
% 1.14/1.31 (~r(s(z), s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[858, 6344, 254])).
% 1.14/1.31 tff(6346,plain,
% 1.14/1.31 (b(s(z), s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[467, 6345, 6209])).
% 1.14/1.31 tff(6347,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6348,plain,
% 1.14/1.31 (((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6349,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[6348])).
% 1.14/1.31 tff(6350,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[6349, 6347])).
% 1.14/1.31 tff(6351,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(z), z)) | (~r(s(elem!1), s(z))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(6352,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))) | (~r(s(z), z))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[6351, 6350])).
% 1.14/1.31 tff(6353,plain,
% 1.14/1.31 (~r(s(elem!1), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6352, 180, 270, 780])).
% 1.14/1.31 tff(6354,plain,
% 1.14/1.31 (b(s(elem!1), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1652, 6353, 1228])).
% 1.14/1.31 tff(6355,plain,
% 1.14/1.31 (~r(s(s(elem!1)), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[3724, 780, 607, 874, 270])).
% 1.14/1.31 tff(6356,plain,
% 1.14/1.31 (b(s(s(elem!1)), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[228, 6355])).
% 1.14/1.31 tff(6357,plain,
% 1.14/1.31 (~b(z, elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[3920, 6356, 441, 911, 27])).
% 1.14/1.31 tff(6358,plain,
% 1.14/1.31 (r(z, elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[556, 6357, 109])).
% 1.14/1.31 tff(6359,plain,
% 1.14/1.31 (~r(s(z), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[4984, 6358, 780])).
% 1.14/1.31 tff(6360,plain,
% 1.14/1.31 (b(s(z), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[193, 6359, 156])).
% 1.14/1.31 tff(6361,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6362,plain,
% 1.14/1.31 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6363,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[6362])).
% 1.14/1.31 tff(6364,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[6363, 6361])).
% 1.14/1.31 tff(6365,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(6366,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[6365, 6364])).
% 1.14/1.31 tff(6367,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6366, 206, 1168, 6360, 6354])).
% 1.14/1.31 tff(6368,plain,((~r(s(z), z)) | (~b(s(elem!1), elem!1)) | (s(z) = elem!1) | (z = elem!1) | (~r(elem!1, s(z))) | (~b(z, s(z))) | (elem!1 = s(s(elem!1))) | (~b(s(z), s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(6369,plain,
% 1.14/1.31 (~r(s(z), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6368, 6346, 6194, 441, 5773, 6202, 517, 6342, 270])).
% 1.14/1.31 tff(6370,plain,
% 1.14/1.31 (b(s(z), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[794, 6369])).
% 1.14/1.31 tff(6371,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6372,plain,
% 1.14/1.31 (((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6373,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[6372])).
% 1.14/1.31 tff(6374,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[6373, 6371])).
% 1.14/1.31 tff(6375,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(6376,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[6375, 6374])).
% 1.14/1.31 tff(6377,plain,
% 1.14/1.31 (~b(s(s(s(s(z)))), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6376, 206, 6370, 6346, 6208])).
% 1.14/1.31 tff(6378,plain,
% 1.14/1.31 (r(s(s(s(s(z)))), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[5878, 150, 1050, 6377])).
% 1.14/1.31 tff(6379,plain,
% 1.14/1.31 (~b(s(z), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[4974, 206, 335, 6346])).
% 1.14/1.31 tff(6380,plain,
% 1.14/1.31 (r(s(z), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[193, 6379, 5773])).
% 1.14/1.31 tff(6381,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[5874, 180, 6380, 6204, 6378])).
% 1.14/1.31 tff(6382,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(elem!1))) | (~r(elem!1, s(z))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(z))) | (~(s(s(s(elem!1))) = elem!1)) | r(s(s(s(s(s(elem!1))))), elem!1) | (s(elem!1) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(6383,plain,
% 1.14/1.31 (~r(s(elem!1), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6382, 5793, 6177, 254, 6184, 5757, 6157, 18])).
% 1.14/1.31 tff(6384,plain,
% 1.14/1.31 (b(s(elem!1), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[283, 6383])).
% 1.14/1.31 tff(6385,plain,
% 1.14/1.31 (~b(s(elem!1), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6111, 6384, 5757, 11, 5801, 6177])).
% 1.14/1.31 tff(6386,plain,
% 1.14/1.31 (~r(s(elem!1), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[3897, 441, 170])).
% 1.14/1.31 tff(6387,plain,
% 1.14/1.31 (~b(s(z), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[4002, 95, 3900])).
% 1.14/1.31 tff(6388,plain,
% 1.14/1.31 (r(s(z), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[794, 6387])).
% 1.14/1.31 tff(6389,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6390,plain,
% 1.14/1.31 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6391,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[6390])).
% 1.14/1.31 tff(6392,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[6391, 6389])).
% 1.14/1.31 tff(6393,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(6394,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[6393, 6392])).
% 1.14/1.31 tff(6395,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6394, 206, 335, 653, 95])).
% 1.14/1.31 tff(6396,plain,((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(6397,plain,
% 1.14/1.31 (~b(elem!1, z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6396, 95, 335])).
% 1.14/1.31 tff(6398,plain,
% 1.14/1.31 (r(elem!1, z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[387, 6397, 135])).
% 1.14/1.31 tff(6399,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[4016, 180, 6398, 441, 6388])).
% 1.14/1.31 tff(6400,plain,((~b(s(elem!1), z)) | (~r(elem!1, s(z))) | (elem!1 = z) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(6401,plain,
% 1.14/1.31 (~b(s(elem!1), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6400, 441, 620, 335, 95])).
% 1.14/1.31 tff(6402,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1652, 6401, 6386, 99])).
% 1.14/1.31 tff(6403,plain,((~r(elem!1, s(z))) | (s(elem!1) = s(z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(6404,plain,
% 1.14/1.31 (~r(s(elem!1), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6403, 6384, 5793, 5782, 6177])).
% 1.14/1.31 tff(6405,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[167, 6404, 6385, 38])).
% 1.14/1.31 tff(6406,plain,((~b(s(s(s(elem!1))), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1)) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(6407,plain,
% 1.14/1.31 (~b(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6406, 254, 11])).
% 1.14/1.31 tff(6408,plain,
% 1.14/1.31 (r(s(s(s(elem!1))), s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[293, 6407, 11])).
% 1.14/1.31 tff(6409,plain,
% 1.14/1.31 (r(s(s(s(elem!1))), s(elem!1)) <=> r(elem!1, s(elem!1))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[5757])).
% 1.14/1.31 tff(6410,plain,
% 1.14/1.31 (r(elem!1, s(elem!1))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[6408, 6409])).
% 1.14/1.31 tff(6411,plain,
% 1.14/1.31 (~r(elem!1, s(s(elem!1)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[408, 180, 6410, 254])).
% 1.14/1.31 tff(6412,plain,
% 1.14/1.31 (b(elem!1, s(s(elem!1)))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[889, 6411, 24])).
% 1.14/1.31 tff(6413,plain,
% 1.14/1.31 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 1.14/1.31 inference(monotonicity,[status(thm)],[2883])).
% 1.14/1.31 tff(6414,plain,
% 1.14/1.31 (b(elem!1, z)),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[4849, 6413])).
% 1.14/1.31 tff(6415,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2809, 206, 6414, 5827, 509])).
% 1.14/1.31 tff(6416,plain,((~r(s(elem!1), z)) | (~b(elem!1, s(s(elem!1)))) | (~(s(s(s(elem!1))) = elem!1)) | (~r(s(s(s(elem!1))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(6417,plain,
% 1.14/1.31 (~r(s(elem!1), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6416, 6412, 5757, 6408, 254])).
% 1.14/1.31 tff(6418,plain,
% 1.14/1.31 (b(s(elem!1), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[283, 6417])).
% 1.14/1.31 tff(6419,plain,
% 1.14/1.31 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[5796])).
% 1.14/1.31 tff(6420,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6421,plain,
% 1.14/1.31 (((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6422,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[6421])).
% 1.14/1.31 tff(6423,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[6422, 6420])).
% 1.14/1.31 tff(6424,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(6425,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[6424, 6423])).
% 1.14/1.31 tff(6426,plain,
% 1.14/1.31 (~r(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6425, 180, 6410, 254])).
% 1.14/1.31 tff(6427,plain,
% 1.14/1.31 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[6426, 6419])).
% 1.14/1.31 tff(6428,plain,
% 1.14/1.31 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2377, 6427, 5791])).
% 1.14/1.31 tff(6429,plain,
% 1.14/1.31 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6167, 6428, 5757])).
% 1.14/1.31 tff(6430,plain,
% 1.14/1.31 (~r(s(z), s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[5015, 6429, 254, 6408])).
% 1.14/1.31 tff(6431,plain,
% 1.14/1.31 (b(s(z), s(elem!1))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[467, 6430, 5783])).
% 1.14/1.31 tff(6432,plain,
% 1.14/1.31 (b(s(s(elem!1)), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[267, 150, 6426, 30])).
% 1.14/1.31 tff(6433,plain,
% 1.14/1.31 (~b(s(elem!1), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6111, 441, 5757, 11, 5801, 95])).
% 1.14/1.31 tff(6434,plain,
% 1.14/1.31 (r(s(elem!1), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[167, 6433, 38])).
% 1.14/1.31 tff(6435,plain,
% 1.14/1.31 (~r(s(elem!1), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[3897, 6434, 441])).
% 1.14/1.31 tff(6436,plain,
% 1.14/1.31 (b(s(elem!1), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[1652, 6435, 5782])).
% 1.14/1.31 tff(6437,plain,
% 1.14/1.31 (~r(z, elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6054, 441, 5757, 38, 607, 5782, 95])).
% 1.14/1.31 tff(6438,plain,
% 1.14/1.31 (b(z, elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[556, 6437, 5801])).
% 1.14/1.31 tff(6439,plain,
% 1.14/1.31 (~b(s(s(s(s(z)))), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2770, 6438, 2742, 5813])).
% 1.14/1.31 tff(6440,plain,
% 1.14/1.31 (r(s(s(s(s(z)))), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[5892, 6439, 5776])).
% 1.14/1.31 tff(6441,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6442,plain,
% 1.14/1.31 (((~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z))) <=> ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6443,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[6442])).
% 1.14/1.31 tff(6444,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[6443, 6441])).
% 1.14/1.31 tff(6445,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z)))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(6446,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(elem!1))))), z))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[6445, 6444])).
% 1.14/1.31 tff(6447,plain,
% 1.14/1.31 (~b(s(s(s(s(s(elem!1))))), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6446, 206, 797, 3363])).
% 1.14/1.31 tff(6448,plain,
% 1.14/1.31 (r(s(s(s(s(s(elem!1))))), z)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2388, 150, 1395, 6447])).
% 1.14/1.31 tff(6449,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6450,plain,
% 1.14/1.31 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))) <=> ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6451,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, elem!1))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[6450])).
% 1.14/1.31 tff(6452,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, elem!1)))),
% 1.14/1.31 inference(transitivity,[status(thm)],[6451, 6449])).
% 1.14/1.31 tff(6453,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(6454,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(z, s(z))) | (~b(z, elem!1))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[6453, 6452])).
% 1.14/1.31 tff(6455,plain,
% 1.14/1.31 (~b(z, s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6454, 206, 117, 797])).
% 1.14/1.31 tff(6456,plain,
% 1.14/1.31 (r(z, s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[505, 6455])).
% 1.14/1.31 tff(6457,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6458,plain,
% 1.14/1.31 (((~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6459,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z)))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[6458])).
% 1.14/1.31 tff(6460,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.14/1.31 inference(transitivity,[status(thm)],[6459, 6457])).
% 1.14/1.31 tff(6461,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z))))),
% 1.14/1.31 inference(quant_inst,[status(thm)],[])).
% 1.14/1.31 tff(6462,plain,
% 1.14/1.31 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 1.14/1.31 inference(modus_ponens,[status(thm)],[6461, 6460])).
% 1.14/1.31 tff(6463,plain,
% 1.14/1.31 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6462, 206, 117, 3363])).
% 1.14/1.31 tff(6464,plain,
% 1.14/1.31 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[2578, 6463])).
% 1.14/1.31 tff(6465,plain,
% 1.14/1.31 ($false),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[5112, 180, 6464, 6456, 6448])).
% 1.14/1.31 tff(6466,plain,((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(elem!1))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.31 tff(6467,plain,
% 1.14/1.31 (~b(s(z), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[6466, 6438, 3363])).
% 1.14/1.31 tff(6468,plain,
% 1.14/1.31 (r(s(z), elem!1)),
% 1.14/1.31 inference(unit_resolution,[status(thm)],[193, 6467, 5777])).
% 1.14/1.31 tff(6469,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6470,plain,
% 1.14/1.31 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.31 inference(rewrite,[status(thm)],[])).
% 1.14/1.31 tff(6471,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))))),
% 1.14/1.31 inference(monotonicity,[status(thm)],[6470])).
% 1.14/1.31 tff(6472,plain,
% 1.14/1.31 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[6471, 6469])).
% 1.14/1.32 tff(6473,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(6474,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), s(s(s(s(z))))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6473, 6472])).
% 1.14/1.32 tff(6475,plain,
% 1.14/1.32 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6474, 180, 170, 5860])).
% 1.14/1.32 tff(6476,plain,
% 1.14/1.32 (b(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[5905, 150, 5831, 6475])).
% 1.14/1.32 tff(6477,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6478,plain,
% 1.14/1.32 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6479,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6478])).
% 1.14/1.32 tff(6480,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[6479, 6477])).
% 1.14/1.32 tff(6481,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(6482,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6481, 6480])).
% 1.14/1.32 tff(6483,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6482, 206, 3900, 6476, 5879])).
% 1.14/1.32 tff(6484,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), s(z))) | (s(elem!1) = s(s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(6485,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6484, 6468, 6440, 6434, 6436, 5825])).
% 1.14/1.32 tff(6486,plain,((~r(elem!1, s(z))) | (~b(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(elem!1))) | (~b(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(6487,plain,
% 1.14/1.32 (~r(elem!1, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6486, 6428, 6432, 6431, 6418, 11])).
% 1.14/1.32 tff(6488,plain,
% 1.14/1.32 (b(elem!1, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[154, 6487, 5778])).
% 1.14/1.32 tff(6489,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[975, 206, 95, 796, 607])).
% 1.14/1.32 tff(6490,plain,((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(6491,plain,
% 1.14/1.32 (~b(s(z), z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6490, 6418, 6431])).
% 1.14/1.32 tff(6492,plain,
% 1.14/1.32 (r(s(z), z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[794, 6491])).
% 1.14/1.32 tff(6493,plain,
% 1.14/1.32 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[5786])).
% 1.14/1.32 tff(6494,plain,
% 1.14/1.32 ((~(elem!1 = s(s(elem!1)))) <=> (~(elem!1 = s(s(s(s(s(elem!1)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[5788])).
% 1.14/1.32 tff(6495,plain,
% 1.14/1.32 (~(elem!1 = s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[24, 6494])).
% 1.14/1.32 tff(6496,plain,
% 1.14/1.32 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(elem!1)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[5786])).
% 1.14/1.32 tff(6497,plain,
% 1.14/1.32 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[6496])).
% 1.14/1.32 tff(6498,plain,
% 1.14/1.32 ((~r(elem!1, s(s(elem!1)))) <=> (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6497])).
% 1.14/1.32 tff(6499,plain,
% 1.14/1.32 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6411, 6498])).
% 1.14/1.32 tff(6500,plain,
% 1.14/1.32 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[3488, 6499, 6495])).
% 1.14/1.32 tff(6501,plain,
% 1.14/1.32 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[3498, 6488, 6500])).
% 1.14/1.32 tff(6502,plain,
% 1.14/1.32 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2578, 6501])).
% 1.14/1.32 tff(6503,plain,
% 1.14/1.32 (r(s(s(elem!1)), s(z))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6502, 6493])).
% 1.14/1.32 tff(6504,plain,
% 1.14/1.32 (~r(s(s(elem!1)), z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[789, 6503, 6492])).
% 1.14/1.32 tff(6505,plain,
% 1.14/1.32 (b(s(s(elem!1)), z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[228, 6504])).
% 1.14/1.32 tff(6506,plain,
% 1.14/1.32 (~b(z, elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[3706, 6505, 6432])).
% 1.14/1.32 tff(6507,plain,
% 1.14/1.32 (r(z, elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[556, 6506, 5801])).
% 1.14/1.32 tff(6508,plain,
% 1.14/1.32 (~r(s(z), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[4984, 6507, 6492])).
% 1.14/1.32 tff(6509,plain,
% 1.14/1.32 (b(s(z), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[193, 6508, 5777])).
% 1.14/1.32 tff(6510,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6511,plain,
% 1.14/1.32 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6512,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6511])).
% 1.14/1.32 tff(6513,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[6512, 6510])).
% 1.14/1.32 tff(6514,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), z)) | (~b(s(z), s(s(elem!1)))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(6515,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6514, 6513])).
% 1.14/1.32 tff(6516,plain,
% 1.14/1.32 (~b(s(z), s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6515, 206, 6509, 6432, 6505])).
% 1.14/1.32 tff(6517,plain,
% 1.14/1.32 ((s(z) = s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[5947, 150, 6516])).
% 1.14/1.32 tff(6518,plain,
% 1.14/1.32 (r(s(z), s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6517, 5935])).
% 1.14/1.32 tff(6519,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 1.14/1.32 tff(6520,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6521,plain,
% 1.14/1.32 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6522,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6521])).
% 1.14/1.32 tff(6523,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[6522, 6520])).
% 1.14/1.32 tff(6524,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(6525,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6524, 6523])).
% 1.14/1.32 tff(6526,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6525, 206, 95, 196, 6519])).
% 1.14/1.32 tff(6527,plain,((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(6528,plain,
% 1.14/1.32 (~b(s(elem!1), s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6527, 6505, 6418])).
% 1.14/1.32 tff(6529,plain,
% 1.14/1.32 (r(s(elem!1), s(s(elem!1)))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[692, 6528, 2611])).
% 1.14/1.32 tff(6530,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6531,plain,
% 1.14/1.32 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6532,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6531])).
% 1.14/1.32 tff(6533,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[6532, 6530])).
% 1.14/1.32 tff(6534,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(6535,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6534, 6533])).
% 1.14/1.32 tff(6536,plain,
% 1.14/1.32 (~r(s(elem!1), s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6535, 180, 6529, 6518])).
% 1.14/1.32 tff(6537,plain,
% 1.14/1.32 (b(s(elem!1), s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1652, 6536, 5782])).
% 1.14/1.32 tff(6538,plain,
% 1.14/1.32 (~b(s(elem!1), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[4939, 6537, 6488])).
% 1.14/1.32 tff(6539,plain,
% 1.14/1.32 (r(s(elem!1), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[167, 6538, 38])).
% 1.14/1.32 tff(6540,plain,
% 1.14/1.32 (~r(s(s(s(s(z)))), z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6101, 180, 543, 5860])).
% 1.14/1.32 tff(6541,plain,
% 1.14/1.32 (b(s(s(s(s(z)))), z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2740, 150, 2737, 6540])).
% 1.14/1.32 tff(6542,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6543,plain,
% 1.14/1.32 (((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6544,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6543])).
% 1.14/1.32 tff(6545,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[6544, 6542])).
% 1.14/1.32 tff(6546,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z)))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(6547,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), s(s(s(s(z))))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6546, 6545])).
% 1.14/1.32 tff(6548,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6547, 206, 95, 6541, 6476])).
% 1.14/1.32 tff(6549,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(6550,plain,
% 1.14/1.32 (~r(s(s(s(s(z)))), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6549, 6418, 5825, 6507, 6539])).
% 1.14/1.32 tff(6551,plain,
% 1.14/1.32 (b(s(s(s(s(z)))), elem!1)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[5892, 6550, 5776])).
% 1.14/1.32 tff(6552,plain,
% 1.14/1.32 (~b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2748, 206, 6432, 6551])).
% 1.14/1.32 tff(6553,plain,
% 1.14/1.32 (r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2753, 150, 5813, 6552])).
% 1.14/1.32 tff(6554,plain,
% 1.14/1.32 (~b(s(s(s(s(z)))), s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6121, 206, 6509, 6551])).
% 1.14/1.32 tff(6555,plain,
% 1.14/1.32 (r(s(s(s(s(z)))), s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[5878, 150, 1050, 6554])).
% 1.14/1.32 tff(6556,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6557,plain,
% 1.14/1.32 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))) <=> ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6558,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6557])).
% 1.14/1.32 tff(6559,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[6558, 6556])).
% 1.14/1.32 tff(6560,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(6561,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(elem!1)), s(s(s(s(z))))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6560, 6559])).
% 1.14/1.32 tff(6562,plain,
% 1.14/1.32 ($false),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6561, 180, 6503, 6555, 6553])).
% 1.14/1.32 tff(6563,plain,((~r(s(s(elem!1)), s(elem!1))) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.32 tff(6564,plain,
% 1.14/1.32 (~r(s(s(elem!1)), s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6563, 11])).
% 1.14/1.32 tff(6565,plain,
% 1.14/1.32 (b(s(s(elem!1)), s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[605, 6564, 57])).
% 1.14/1.32 tff(6566,assumption,(~(elem!1 = s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 1.14/1.32 tff(6567,plain,
% 1.14/1.32 (b(s(s(s(s(s(s(elem!1)))))), z) <=> b(elem!1, z)),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6210])).
% 1.14/1.32 tff(6568,plain,
% 1.14/1.32 (b(elem!1, z) <=> b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.14/1.32 inference(symmetry,[status(thm)],[6567])).
% 1.14/1.32 tff(6569,plain,
% 1.14/1.32 (~r(elem!1, z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[650, 170, 270])).
% 1.14/1.32 tff(6570,plain,
% 1.14/1.32 (b(elem!1, z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[387, 6569, 6195])).
% 1.14/1.32 tff(6571,plain,
% 1.14/1.32 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6570, 6568])).
% 1.14/1.32 tff(6572,plain,
% 1.14/1.32 (b(s(s(s(s(s(s(elem!1)))))), s(z)) <=> b(elem!1, s(z))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6210])).
% 1.14/1.32 tff(6573,plain,
% 1.14/1.32 (b(elem!1, s(z)) <=> b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.14/1.32 inference(symmetry,[status(thm)],[6572])).
% 1.14/1.32 tff(6574,plain,
% 1.14/1.32 (~(elem!1 = s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[162, 5773])).
% 1.14/1.32 tff(6575,plain,
% 1.14/1.32 (b(elem!1, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[154, 91, 6574])).
% 1.14/1.32 tff(6576,plain,
% 1.14/1.32 (b(s(s(s(s(s(s(elem!1)))))), s(z))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6575, 6573])).
% 1.14/1.32 tff(6577,plain,
% 1.14/1.32 (~b(s(z), z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1064, 6576, 6571])).
% 1.14/1.32 tff(6578,plain,
% 1.14/1.32 (r(s(z), z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[794, 6577])).
% 1.14/1.32 tff(6579,plain,
% 1.14/1.32 (b(elem!1, z) <=> b(s(s(s(elem!1))), z)),
% 1.14/1.32 inference(symmetry,[status(thm)],[6413])).
% 1.14/1.32 tff(6580,plain,
% 1.14/1.32 (b(s(s(s(elem!1))), z)),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6570, 6579])).
% 1.14/1.32 tff(6581,plain,
% 1.14/1.32 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[2883])).
% 1.14/1.32 tff(6582,plain,
% 1.14/1.32 (b(elem!1, s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 1.14/1.32 inference(symmetry,[status(thm)],[6581])).
% 1.14/1.32 tff(6583,plain,
% 1.14/1.32 (b(s(s(s(elem!1))), s(z))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6575, 6582])).
% 1.14/1.32 tff(6584,plain,
% 1.14/1.32 (b(s(z), s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[3142, 6583, 270, 170, 6580, 91])).
% 1.14/1.32 tff(6585,plain,
% 1.14/1.32 (~r(s(s(elem!1)), z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[3724, 6584, 270, 5429, 6578])).
% 1.14/1.32 tff(6586,plain,
% 1.14/1.32 (b(s(s(elem!1)), z)),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[228, 6585])).
% 1.14/1.32 tff(6587,plain,
% 1.14/1.32 (~b(z, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[4505, 6575, 6570])).
% 1.14/1.32 tff(6588,plain,
% 1.14/1.32 (r(z, s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[505, 6587])).
% 1.14/1.32 tff(6589,plain,
% 1.14/1.32 (~r(s(elem!1), s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[3782, 6588, 270])).
% 1.14/1.32 tff(6590,plain,
% 1.14/1.32 (b(s(elem!1), s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[1652, 6589, 6193])).
% 1.14/1.32 tff(6591,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6592,plain,
% 1.14/1.32 (((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6593,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z)))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6592])).
% 1.14/1.32 tff(6594,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[6593, 6591])).
% 1.14/1.32 tff(6595,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(elem!1, s(z))) | (~b(s(elem!1), s(z))) | (~b(elem!1, s(elem!1))))),
% 1.14/1.32 inference(quant_inst,[status(thm)],[])).
% 1.14/1.32 tff(6596,plain,
% 1.14/1.32 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), s(z)))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6595, 6594])).
% 1.14/1.32 tff(6597,plain,
% 1.14/1.32 (~b(elem!1, s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6596, 206, 6575, 6590])).
% 1.14/1.32 tff(6598,plain,
% 1.14/1.32 (r(elem!1, s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[401, 6597, 54])).
% 1.14/1.32 tff(6599,plain,
% 1.14/1.32 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(elem!1))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[1025])).
% 1.14/1.32 tff(6600,plain,
% 1.14/1.32 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.32 inference(symmetry,[status(thm)],[6599])).
% 1.14/1.32 tff(6601,plain,
% 1.14/1.32 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 1.14/1.32 inference(transitivity,[status(thm)],[72, 6600, 1023])).
% 1.14/1.32 tff(6602,plain,
% 1.14/1.32 (r(elem!1, s(s(elem!1))) <=> r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6601])).
% 1.14/1.32 tff(6603,plain,
% 1.14/1.32 (r(elem!1, s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(elem!1)))),
% 1.14/1.32 inference(symmetry,[status(thm)],[6602])).
% 1.14/1.32 tff(6604,plain,
% 1.14/1.32 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 1.14/1.32 inference(transitivity,[status(thm)],[1096, 6599, 71])).
% 1.14/1.32 tff(6605,plain,
% 1.14/1.32 (r(s(s(s(s(s(elem!1))))), s(z)) <=> r(s(s(elem!1)), s(z))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6604])).
% 1.14/1.32 tff(6606,plain,
% 1.14/1.32 (r(s(s(elem!1)), s(z)) <=> r(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.32 inference(symmetry,[status(thm)],[6605])).
% 1.14/1.32 tff(6607,plain,
% 1.14/1.32 ((~r(s(s(elem!1)), s(z))) <=> (~r(s(s(s(s(s(elem!1))))), s(z)))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6606])).
% 1.14/1.32 tff(6608,plain,
% 1.14/1.32 (~r(z, s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[939, 543, 442])).
% 1.14/1.32 tff(6609,plain,
% 1.14/1.32 ((z = s(elem!1)) | b(z, s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[817, 150, 6608])).
% 1.14/1.32 tff(6610,plain,
% 1.14/1.32 (b(z, s(elem!1))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[6609, 927])).
% 1.14/1.32 tff(6611,plain,
% 1.14/1.32 ((~r(elem!1, s(s(elem!1)))) <=> (~r(elem!1, s(s(s(s(s(elem!1)))))))),
% 1.14/1.32 inference(monotonicity,[status(thm)],[6602])).
% 1.14/1.32 tff(6612,plain,
% 1.14/1.32 (~r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[4363, 6611])).
% 1.14/1.32 tff(6613,plain,
% 1.14/1.32 (b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[3488, 6612, 6566])).
% 1.14/1.32 tff(6614,plain,
% 1.14/1.32 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[3498, 6613, 157])).
% 1.14/1.32 tff(6615,plain,
% 1.14/1.32 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.32 inference(unit_resolution,[status(thm)],[2578, 6614])).
% 1.14/1.32 tff(6616,plain,
% 1.14/1.32 (r(s(s(elem!1)), s(z))),
% 1.14/1.32 inference(modus_ponens,[status(thm)],[6615, 6605])).
% 1.14/1.32 tff(6617,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6618,plain,
% 1.14/1.32 (((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.14/1.32 inference(rewrite,[status(thm)],[])).
% 1.14/1.32 tff(6619,plain,
% 1.14/1.32 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6618])).
% 1.14/1.33 tff(6620,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z)))),
% 1.14/1.33 inference(transitivity,[status(thm)],[6619, 6617])).
% 1.14/1.33 tff(6621,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(6622,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6621, 6620])).
% 1.14/1.33 tff(6623,plain,
% 1.14/1.33 (~r(s(s(elem!1)), z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6622, 180, 543, 6616, 485])).
% 1.14/1.33 tff(6624,plain,
% 1.14/1.33 (b(s(s(elem!1)), z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[228, 6623])).
% 1.14/1.33 tff(6625,plain,
% 1.14/1.33 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6601])).
% 1.14/1.33 tff(6626,plain,
% 1.14/1.33 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.14/1.33 inference(symmetry,[status(thm)],[6625])).
% 1.14/1.33 tff(6627,plain,
% 1.14/1.33 (r(s(s(elem!1)), elem!1) <=> r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6601])).
% 1.14/1.33 tff(6628,plain,
% 1.14/1.33 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6627])).
% 1.14/1.33 tff(6629,plain,
% 1.14/1.33 (~r(s(s(elem!1)), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6425, 180, 442, 254])).
% 1.14/1.33 tff(6630,plain,
% 1.14/1.33 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6629, 6628])).
% 1.14/1.33 tff(6631,plain,
% 1.14/1.33 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2377, 6630, 3061])).
% 1.14/1.33 tff(6632,plain,
% 1.14/1.33 (b(s(s(elem!1)), elem!1)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6631, 6626])).
% 1.14/1.33 tff(6633,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[3199, 206, 653, 6632, 6624])).
% 1.14/1.33 tff(6634,plain,((~r(s(s(elem!1)), s(elem!1))) | (~b(elem!1, z)) | (~r(z, elem!1)) | (~r(z, s(z))) | (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(z))) | (s(s(s(s(s(elem!1))))) = elem!1) | (elem!1 = s(s(s(s(s(elem!1)))))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(6635,plain,
% 1.14/1.33 (~r(s(s(elem!1)), s(elem!1))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6634, 543, 653, 485, 1024, 157, 3061, 6566, 442])).
% 1.14/1.33 tff(6636,plain,
% 1.14/1.33 (b(s(s(elem!1)), s(elem!1))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[605, 6635, 74])).
% 1.14/1.33 tff(6637,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6638,plain,
% 1.14/1.33 (((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6639,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6638])).
% 1.14/1.33 tff(6640,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[6639, 6637])).
% 1.14/1.33 tff(6641,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(6642,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6641, 6640])).
% 1.14/1.33 tff(6643,plain,
% 1.14/1.33 (~b(s(s(elem!1)), z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6642, 206, 6636, 6610])).
% 1.14/1.33 tff(6644,plain,
% 1.14/1.33 (r(s(s(elem!1)), z)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[228, 6643])).
% 1.14/1.33 tff(6645,plain,
% 1.14/1.33 (~r(s(s(elem!1)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[787, 180, 780, 6644])).
% 1.14/1.33 tff(6646,plain,
% 1.14/1.33 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6645, 6607])).
% 1.14/1.33 tff(6647,plain,
% 1.14/1.33 (b(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2578, 6646])).
% 1.14/1.33 tff(6648,plain,
% 1.14/1.33 (~b(elem!1, s(s(s(s(s(elem!1))))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[3498, 6647, 157])).
% 1.14/1.33 tff(6649,plain,
% 1.14/1.33 (r(elem!1, s(s(s(s(s(elem!1))))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[3488, 6648, 6566])).
% 1.14/1.33 tff(6650,plain,
% 1.14/1.33 (r(elem!1, s(s(elem!1)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6649, 6603])).
% 1.14/1.33 tff(6651,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6652,plain,
% 1.14/1.33 (((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1))))) <=> ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6653,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6652])).
% 1.14/1.33 tff(6654,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[6653, 6651])).
% 1.14/1.33 tff(6655,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1)))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(6656,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(z, s(s(elem!1))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6655, 6654])).
% 1.14/1.33 tff(6657,plain,
% 1.14/1.33 (~b(z, s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6656, 206, 6636, 6610])).
% 1.14/1.33 tff(6658,plain,
% 1.14/1.33 (r(z, s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2185, 6657])).
% 1.14/1.33 tff(6659,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6660,plain,
% 1.14/1.33 (((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6661,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6660])).
% 1.14/1.33 tff(6662,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[6661, 6659])).
% 1.14/1.33 tff(6663,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(z, elem!1)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(6664,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(elem!1, s(s(elem!1))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6663, 6662])).
% 1.14/1.33 tff(6665,plain,
% 1.14/1.33 (~r(elem!1, s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6664, 180, 543, 6658])).
% 1.14/1.33 tff(6666,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6665, 6650])).
% 1.14/1.33 tff(6667,plain,((~r(z, elem!1)) | (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) | (elem!1 = s(s(s(s(s(elem!1)))))) | (~b(elem!1, s(z))) | (~r(s(z), z)) | (s(s(elem!1)) = s(elem!1)) | (~b(elem!1, z)) | (~r(z, s(z))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(6668,plain,
% 1.14/1.33 (~r(z, elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6667, 6578, 5808, 6566, 6570, 5429, 6575, 6588, 3061, 6598])).
% 1.14/1.33 tff(6669,plain,
% 1.14/1.33 (b(z, elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[556, 6668, 6194])).
% 1.14/1.33 tff(6670,plain,
% 1.14/1.33 (~b(s(s(elem!1)), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[3706, 6669, 6586])).
% 1.14/1.33 tff(6671,plain,
% 1.14/1.33 (r(s(s(elem!1)), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[267, 150, 6670, 4543])).
% 1.14/1.33 tff(6672,plain,
% 1.14/1.33 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6161])).
% 1.14/1.33 tff(6673,plain,
% 1.14/1.33 (b(s(s(elem!1)), s(z)) <=> b(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.33 inference(symmetry,[status(thm)],[6672])).
% 1.14/1.33 tff(6674,plain,
% 1.14/1.33 ((~b(s(s(elem!1)), s(z))) <=> (~b(s(s(s(s(s(elem!1))))), s(z)))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6673])).
% 1.14/1.33 tff(6675,plain,
% 1.14/1.33 (~b(s(s(elem!1)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[615, 6584, 195])).
% 1.14/1.33 tff(6676,plain,
% 1.14/1.33 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6675, 6674])).
% 1.14/1.33 tff(6677,plain,
% 1.14/1.33 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2578, 6676])).
% 1.14/1.33 tff(6678,plain,
% 1.14/1.33 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(symmetry,[status(thm)],[6162])).
% 1.14/1.33 tff(6679,plain,
% 1.14/1.33 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6678])).
% 1.14/1.33 tff(6680,plain,
% 1.14/1.33 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6670, 6679])).
% 1.14/1.33 tff(6681,plain,
% 1.14/1.33 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2377, 6680, 3061])).
% 1.14/1.33 tff(6682,plain,
% 1.14/1.33 (~r(s(z), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2956, 6681, 6677])).
% 1.14/1.33 tff(6683,plain,
% 1.14/1.33 (b(s(z), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[193, 6682, 5773])).
% 1.14/1.33 tff(6684,plain,
% 1.14/1.33 (~(s(elem!1) = s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[680, 5429])).
% 1.14/1.33 tff(6685,plain,
% 1.14/1.33 (r(s(s(elem!1)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[778, 6675])).
% 1.14/1.33 tff(6686,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6687,plain,
% 1.14/1.33 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6688,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6687])).
% 1.14/1.33 tff(6689,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1)))),
% 1.14/1.33 inference(transitivity,[status(thm)],[6688, 6686])).
% 1.14/1.33 tff(6690,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(6691,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), elem!1))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6690, 6689])).
% 1.14/1.33 tff(6692,plain,
% 1.14/1.33 (~r(s(elem!1), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6691, 180, 170, 6685, 6671])).
% 1.14/1.33 tff(6693,plain,
% 1.14/1.33 (b(s(elem!1), s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[692, 6692, 6684])).
% 1.14/1.33 tff(6694,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6695,plain,
% 1.14/1.33 (((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6696,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6695])).
% 1.14/1.33 tff(6697,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[6696, 6694])).
% 1.14/1.33 tff(6698,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(z, s(s(elem!1)))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(6699,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(elem!1)), s(z)))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6698, 6697])).
% 1.14/1.33 tff(6700,plain,
% 1.14/1.33 (~r(z, s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6699, 180, 6685, 6588])).
% 1.14/1.33 tff(6701,plain,
% 1.14/1.33 (b(z, s(s(elem!1)))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2185, 6700])).
% 1.14/1.33 tff(6702,plain,
% 1.14/1.33 (~b(z, s(elem!1))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[3217, 206, 6701, 6693])).
% 1.14/1.33 tff(6703,plain,
% 1.14/1.33 (r(z, s(elem!1))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[817, 150, 6702, 235])).
% 1.14/1.33 tff(6704,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 1.14/1.33 tff(6705,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6706,plain,
% 1.14/1.33 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6707,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6706])).
% 1.14/1.33 tff(6708,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.33 inference(transitivity,[status(thm)],[6707, 6705])).
% 1.14/1.33 tff(6709,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(6710,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6709, 6708])).
% 1.14/1.33 tff(6711,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6710, 180, 6704, 485, 6123, 2741])).
% 1.14/1.33 tff(6712,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(z, s(elem!1))) | (~r(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(6713,plain,
% 1.14/1.33 (~b(s(s(s(s(z)))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6712, 6703, 6588, 6669, 6683])).
% 1.14/1.33 tff(6714,plain,
% 1.14/1.33 (r(s(s(s(s(z)))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[5892, 6713, 5968])).
% 1.14/1.33 tff(6715,plain,
% 1.14/1.33 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[5866, 180, 6714, 6671])).
% 1.14/1.33 tff(6716,plain,
% 1.14/1.33 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2753, 150, 6012, 6715])).
% 1.14/1.33 tff(6717,plain,
% 1.14/1.33 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6474, 180, 170, 6714])).
% 1.14/1.33 tff(6718,plain,
% 1.14/1.33 (b(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[5905, 150, 6011, 6717])).
% 1.14/1.33 tff(6719,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6720,plain,
% 1.14/1.33 (((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6721,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6720])).
% 1.14/1.33 tff(6722,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.33 inference(transitivity,[status(thm)],[6721, 6719])).
% 1.14/1.33 tff(6723,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.33 inference(quant_inst,[status(thm)],[])).
% 1.14/1.33 tff(6724,plain,
% 1.14/1.33 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6723, 6722])).
% 1.14/1.33 tff(6725,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6724, 206, 195, 6718, 6716])).
% 1.14/1.33 tff(6726,plain,(r(elem!1, s(z)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)) | (s(s(s(s(s(elem!1))))) = elem!1) | (s(s(elem!1)) = elem!1) | (elem!1 = s(s(s(s(s(elem!1)))))) | (~r(s(elem!1), z)) | (elem!1 = s(elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(6727,plain,
% 1.14/1.33 (r(elem!1, s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6726, 170, 195, 3061, 4543, 6566, 270, 54, 2883])).
% 1.14/1.33 tff(6728,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[3928, 180, 170, 543, 270])).
% 1.14/1.33 tff(6729,plain,((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(6730,plain,
% 1.14/1.33 (~r(z, elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6729, 170, 270])).
% 1.14/1.33 tff(6731,plain,
% 1.14/1.33 (b(z, elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[556, 6730, 6194])).
% 1.14/1.33 tff(6732,plain,
% 1.14/1.33 (~r(s(z), s(elem!1))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[3593, 6731, 5773, 170, 270])).
% 1.14/1.33 tff(6733,plain,
% 1.14/1.33 (b(s(z), s(elem!1))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[467, 6732, 6209])).
% 1.14/1.33 tff(6734,plain,
% 1.14/1.33 (~b(s(s(elem!1)), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[615, 6733, 195])).
% 1.14/1.33 tff(6735,plain,
% 1.14/1.33 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6734, 6674])).
% 1.14/1.33 tff(6736,plain,
% 1.14/1.33 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2578, 6735])).
% 1.14/1.33 tff(6737,plain,
% 1.14/1.33 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[3332, 6736, 6727])).
% 1.14/1.33 tff(6738,plain,
% 1.14/1.33 (b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2377, 6737, 3061])).
% 1.14/1.33 tff(6739,plain,
% 1.14/1.33 (b(s(s(elem!1)), elem!1)),
% 1.14/1.33 inference(modus_ponens,[status(thm)],[6738, 6162])).
% 1.14/1.33 tff(6740,plain,
% 1.14/1.33 (~r(s(elem!1), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[3897, 6727, 170])).
% 1.14/1.33 tff(6741,plain,
% 1.14/1.33 (b(s(elem!1), s(z))),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[1652, 6740, 6193])).
% 1.14/1.33 tff(6742,plain,
% 1.14/1.33 (~b(s(z), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6466, 6738, 6731])).
% 1.14/1.33 tff(6743,plain,
% 1.14/1.33 (r(s(z), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[193, 6742, 5773])).
% 1.14/1.33 tff(6744,plain,
% 1.14/1.33 (~r(s(s(s(s(z)))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6484, 6743, 170, 6741, 6011])).
% 1.14/1.33 tff(6745,plain,
% 1.14/1.33 (b(s(s(s(s(z)))), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[5892, 6744, 5968])).
% 1.14/1.33 tff(6746,plain,
% 1.14/1.33 (~b(s(s(elem!1)), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[2770, 6745, 6731, 6012])).
% 1.14/1.33 tff(6747,plain,
% 1.14/1.33 ($false),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6746, 6739])).
% 1.14/1.33 tff(6748,plain,((~r(s(elem!1), elem!1)) | (s(s(s(s(s(elem!1))))) = elem!1) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z)) | (s(s(elem!1)) = elem!1) | (elem!1 = s(s(s(s(s(elem!1)))))) | (elem!1 = s(elem!1)) | (~(s(s(s(elem!1))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.33 tff(6749,plain,
% 1.14/1.33 (~r(s(elem!1), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[6748, 270, 6565, 5791, 30, 6495, 46, 5757])).
% 1.14/1.33 tff(6750,plain,
% 1.14/1.33 (b(s(elem!1), elem!1)),
% 1.14/1.33 inference(unit_resolution,[status(thm)],[167, 6749, 38])).
% 1.14/1.33 tff(6751,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6752,plain,
% 1.14/1.33 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.33 inference(rewrite,[status(thm)],[])).
% 1.14/1.33 tff(6753,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.14/1.33 inference(monotonicity,[status(thm)],[6752])).
% 1.14/1.33 tff(6754,plain,
% 1.14/1.33 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[6753, 6751])).
% 1.14/1.34 tff(6755,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(6756,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[6755, 6754])).
% 1.14/1.34 tff(6757,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6756, 206, 1168, 2742, 195])).
% 1.14/1.34 tff(6758,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6759,plain,
% 1.14/1.34 (~b(s(s(elem!1)), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6758, 6750, 6565])).
% 1.14/1.34 tff(6760,plain,
% 1.14/1.34 (r(s(s(elem!1)), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[267, 150, 6759, 30])).
% 1.14/1.34 tff(6761,plain,
% 1.14/1.34 (b(s(s(s(s(s(elem!1))))), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 1.14/1.34 inference(monotonicity,[status(thm)],[5786])).
% 1.14/1.34 tff(6762,plain,
% 1.14/1.34 (b(s(s(elem!1)), elem!1) <=> b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.34 inference(symmetry,[status(thm)],[6761])).
% 1.14/1.34 tff(6763,plain,
% 1.14/1.34 ((~b(s(s(elem!1)), elem!1)) <=> (~b(s(s(s(s(s(elem!1))))), elem!1))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[6762])).
% 1.14/1.34 tff(6764,plain,
% 1.14/1.34 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[6759, 6763])).
% 1.14/1.34 tff(6765,plain,
% 1.14/1.34 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2377, 6764, 5791])).
% 1.14/1.34 tff(6766,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(6767,plain,
% 1.14/1.34 (((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(6768,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[6767])).
% 1.14/1.34 tff(6769,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[6768, 6766])).
% 1.14/1.34 tff(6770,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(6771,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[6770, 6769])).
% 1.14/1.34 tff(6772,plain,
% 1.14/1.34 (~r(s(s(elem!1)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6771, 180, 543, 255])).
% 1.14/1.34 tff(6773,plain,
% 1.14/1.34 (b(s(s(elem!1)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[228, 6772])).
% 1.14/1.34 tff(6774,plain,
% 1.14/1.34 (~(s(elem!1) = s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2881, 1024])).
% 1.14/1.34 tff(6775,plain,
% 1.14/1.34 (~(z = elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[239, 6774])).
% 1.14/1.34 tff(6776,plain,
% 1.14/1.34 (~(s(z) = s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[101, 6774])).
% 1.14/1.34 tff(6777,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6154, 206, 6773, 6541, 5868])).
% 1.14/1.34 tff(6778,plain,((~r(s(s(s(s(z)))), elem!1)) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6779,plain,
% 1.14/1.34 (~r(s(s(s(s(z)))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6778, 543, 2750, 255])).
% 1.14/1.34 tff(6780,plain,
% 1.14/1.34 (b(s(s(s(s(z)))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[5892, 6779, 5828])).
% 1.14/1.34 tff(6781,plain,
% 1.14/1.34 (~b(s(z), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6131, 3774, 5831, 2728, 1168])).
% 1.14/1.34 tff(6782,plain,
% 1.14/1.34 (r(s(z), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[193, 6781, 156])).
% 1.14/1.34 tff(6783,plain,
% 1.14/1.34 (~r(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2956, 6782, 2948])).
% 1.14/1.34 tff(6784,plain,
% 1.14/1.34 (~r(z, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[3782, 3774, 270])).
% 1.14/1.34 tff(6785,plain,
% 1.14/1.34 (b(z, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[505, 6784])).
% 1.14/1.34 tff(6786,plain,
% 1.14/1.34 (~b(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2363, 6785, 196])).
% 1.14/1.34 tff(6787,plain,
% 1.14/1.34 (b(s(s(s(s(s(elem!1))))), s(z)) <=> b(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[6604])).
% 1.14/1.34 tff(6788,plain,
% 1.14/1.34 (b(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[3019, 6787])).
% 1.14/1.34 tff(6789,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[764, 6788])).
% 1.14/1.34 tff(6790,plain,((~b(s(s(s(s(s(elem!1))))), s(z))) | b(s(s(elem!1)), s(z)) | (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6791,plain,
% 1.14/1.34 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6790, 6786, 1024])).
% 1.14/1.34 tff(6792,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2578, 6791, 6783])).
% 1.14/1.34 tff(6793,plain,((~r(s(elem!1), s(z))) | (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~b(s(s(elem!1)), z)) | (s(z) = elem!1) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6794,plain,
% 1.14/1.34 (~r(s(elem!1), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6793, 6773, 2948, 1024, 156, 5831, 6780, 1168, 270])).
% 1.14/1.34 tff(6795,plain,
% 1.14/1.34 (b(s(elem!1), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1652, 6794, 6774])).
% 1.14/1.34 tff(6796,plain,
% 1.14/1.34 (~b(elem!1, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[4939, 6795, 1168])).
% 1.14/1.34 tff(6797,plain,
% 1.14/1.34 (r(elem!1, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[154, 6796, 163])).
% 1.14/1.34 tff(6798,plain,
% 1.14/1.34 (~b(elem!1, s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[5914, 6797, 5831, 1168, 5828, 2750, 270, 156, 255, 6776, 43, 6775, 6773])).
% 1.14/1.34 tff(6799,plain,
% 1.14/1.34 (~r(s(z), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[450, 441, 442])).
% 1.14/1.34 tff(6800,plain,
% 1.14/1.34 (b(s(z), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[467, 6799, 59])).
% 1.14/1.34 tff(6801,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[615, 6800, 5833, 195])).
% 1.14/1.34 tff(6802,plain,((~r(elem!1, s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (s(z) = s(elem!1)) | (~r(elem!1, s(elem!1))) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6803,plain,
% 1.14/1.34 (~r(elem!1, s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6802, 6797, 6776, 195, 255])).
% 1.14/1.34 tff(6804,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[401, 6803, 6798, 5917])).
% 1.14/1.34 tff(6805,plain,((~r(z, elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(s(s(z))))) | (~b(s(elem!1), elem!1)) | (s(s(s(s(z)))) = elem!1) | (s(s(elem!1)) = s(s(s(s(z))))) | (~r(s(elem!1), z)) | (s(z) = elem!1) | (s(elem!1) = elem!1) | (~r(s(s(s(s(s(elem!1))))), elem!1)) | (~(s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6806,plain,
% 1.14/1.34 (~r(z, elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6805, 6760, 6565, 5825, 6750, 5776, 5813, 270, 5777, 38, 6765, 5781])).
% 1.14/1.34 tff(6807,plain,
% 1.14/1.34 (b(z, elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[556, 6806, 5801])).
% 1.14/1.34 tff(6808,plain,
% 1.14/1.34 (~b(s(elem!1), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[4939, 157, 1168])).
% 1.14/1.34 tff(6809,plain,
% 1.14/1.34 (r(s(elem!1), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1652, 6808, 99])).
% 1.14/1.34 tff(6810,plain,
% 1.14/1.34 (~r(z, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[3782, 6809, 270])).
% 1.14/1.34 tff(6811,plain,
% 1.14/1.34 (b(z, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[505, 6810])).
% 1.14/1.34 tff(6812,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[563, 206, 797, 157, 6811])).
% 1.14/1.34 tff(6813,plain,((~b(elem!1, s(z))) | (~b(z, elem!1)) | (~r(s(elem!1), z)) | (s(elem!1) = s(z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6814,plain,
% 1.14/1.34 (~b(elem!1, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6813, 6807, 270, 5782, 6750])).
% 1.14/1.34 tff(6815,plain,
% 1.14/1.34 (r(elem!1, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[154, 6814, 5778])).
% 1.14/1.34 tff(6816,plain,
% 1.14/1.34 (~r(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[3694, 6815, 6760])).
% 1.14/1.34 tff(6817,plain,
% 1.14/1.34 (~b(z, s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[5845, 206, 6750, 797])).
% 1.14/1.34 tff(6818,plain,
% 1.14/1.34 (r(z, s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[817, 150, 6817, 235])).
% 1.14/1.34 tff(6819,plain,
% 1.14/1.34 (~r(s(z), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[3226, 180, 6818, 158])).
% 1.14/1.34 tff(6820,plain,
% 1.14/1.34 (b(s(z), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[794, 6819])).
% 1.14/1.34 tff(6821,plain,
% 1.14/1.34 (~b(s(z), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[805, 6820, 797])).
% 1.14/1.34 tff(6822,plain,
% 1.14/1.34 (r(s(z), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[193, 6821, 5777])).
% 1.14/1.34 tff(6823,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[5912, 180, 270, 6022, 2741])).
% 1.14/1.34 tff(6824,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(elem!1), z)) | (s(elem!1) = s(s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6825,plain,
% 1.14/1.34 (~b(s(s(s(s(z)))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6824, 797, 5825, 270, 6750])).
% 1.14/1.34 tff(6826,plain,
% 1.14/1.34 (r(s(s(s(s(z)))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[5892, 6825, 5776])).
% 1.14/1.34 tff(6827,plain,
% 1.14/1.34 (~b(elem!1, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6813, 797, 270, 5782, 6750])).
% 1.14/1.34 tff(6828,plain,
% 1.14/1.34 (r(elem!1, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[154, 6827, 5778])).
% 1.14/1.34 tff(6829,plain,
% 1.14/1.34 (b(s(s(s(elem!1))), z) <=> b(elem!1, z)),
% 1.14/1.34 inference(monotonicity,[status(thm)],[5757])).
% 1.14/1.34 tff(6830,plain,
% 1.14/1.34 (~r(z, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[5855, 158, 5777, 38, 797, 270])).
% 1.14/1.34 tff(6831,plain,
% 1.14/1.34 (b(z, s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[505, 6830])).
% 1.14/1.34 tff(6832,plain,
% 1.14/1.34 (~b(s(s(elem!1)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[3920, 6831, 6828, 797, 24])).
% 1.14/1.34 tff(6833,plain,
% 1.14/1.34 (r(s(s(elem!1)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[228, 6832])).
% 1.14/1.34 tff(6834,plain,
% 1.14/1.34 (~r(s(s(s(elem!1))), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[3976, 6833, 11, 270])).
% 1.14/1.34 tff(6835,plain,
% 1.14/1.34 (b(s(s(s(elem!1))), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[372, 6834])).
% 1.14/1.34 tff(6836,plain,
% 1.14/1.34 (b(elem!1, z)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[6835, 6829])).
% 1.14/1.34 tff(6837,plain,
% 1.14/1.34 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1)))))) <=> r(elem!1, s(s(elem!1)))),
% 1.14/1.34 inference(transitivity,[status(thm)],[6216, 6218])).
% 1.14/1.34 tff(6838,plain,
% 1.14/1.34 (~(s(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[517, 5981])).
% 1.14/1.34 tff(6839,plain,
% 1.14/1.34 (~b(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[764, 6674])).
% 1.14/1.34 tff(6840,plain,
% 1.14/1.34 (r(s(s(s(s(s(elem!1))))), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2578, 6839])).
% 1.14/1.34 tff(6841,plain,
% 1.14/1.34 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2956, 6840, 169])).
% 1.14/1.34 tff(6842,plain,
% 1.14/1.34 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(s(s(elem!1))))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6335, 6841, 2883, 653, 270, 1168, 6838, 21])).
% 1.14/1.34 tff(6843,plain,
% 1.14/1.34 (r(elem!1, s(s(elem!1)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[6842, 6837])).
% 1.14/1.34 tff(6844,plain,
% 1.14/1.34 (r(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[778, 764])).
% 1.14/1.34 tff(6845,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[4873, 180, 441, 6844, 6843])).
% 1.14/1.34 tff(6846,plain,(b(s(s(elem!1)), s(z)) | (~r(elem!1, s(z))) | (~(s(s(s(elem!1))) = elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), z)) | (~b(s(elem!1), elem!1)) | (s(elem!1) = s(s(s(elem!1)))) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6847,plain,
% 1.14/1.34 (b(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6846, 6822, 5757, 270, 6750, 6836, 18, 6828])).
% 1.14/1.34 tff(6848,plain,
% 1.14/1.34 (~r(s(s(elem!1)), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[5887, 6847, 5813, 6826, 6822])).
% 1.14/1.34 tff(6849,plain,
% 1.14/1.34 (~r(elem!1, s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[450, 158, 6828])).
% 1.14/1.34 tff(6850,plain,
% 1.14/1.34 (b(elem!1, s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[401, 6849, 46])).
% 1.14/1.34 tff(6851,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(6852,plain,
% 1.14/1.34 (((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(6853,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[6852])).
% 1.14/1.34 tff(6854,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[6853, 6851])).
% 1.14/1.34 tff(6855,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(6856,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[6855, 6854])).
% 1.14/1.34 tff(6857,plain,
% 1.14/1.34 (~b(s(s(elem!1)), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6856, 206, 6850, 6565])).
% 1.14/1.34 tff(6858,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[267, 150, 6857, 6848, 30])).
% 1.14/1.34 tff(6859,plain,((~r(s(z), s(elem!1))) | (~r(s(elem!1), z)) | (~b(z, elem!1)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6860,plain,
% 1.14/1.34 (~r(s(z), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6859, 6807, 270, 11])).
% 1.14/1.34 tff(6861,plain,
% 1.14/1.34 (b(s(z), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[467, 6860, 5783])).
% 1.14/1.34 tff(6862,plain,
% 1.14/1.34 (~b(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[615, 6861, 6565])).
% 1.14/1.34 tff(6863,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[778, 6862, 6816])).
% 1.14/1.34 tff(6864,plain,((~r(s(elem!1), z)) | (s(s(s(elem!1))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6865,plain,
% 1.14/1.34 (~r(s(elem!1), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6864, 11])).
% 1.14/1.34 tff(6866,plain,
% 1.14/1.34 (b(s(elem!1), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[283, 6865])).
% 1.14/1.34 tff(6867,plain,
% 1.14/1.34 (~b(s(s(elem!1)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[214, 6866, 6565])).
% 1.14/1.34 tff(6868,plain,
% 1.14/1.34 (r(s(s(elem!1)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[228, 6867])).
% 1.14/1.34 tff(6869,plain,
% 1.14/1.34 (~(elem!1 = z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[287, 5801])).
% 1.14/1.34 tff(6870,plain,
% 1.14/1.34 (~b(s(s(elem!1)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[214, 95, 195])).
% 1.14/1.34 tff(6871,plain,
% 1.14/1.34 (r(s(s(elem!1)), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[228, 6870])).
% 1.14/1.34 tff(6872,plain,
% 1.14/1.34 ((~b(s(s(s(elem!1))), s(z))) <=> (~b(elem!1, s(z)))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[6581])).
% 1.14/1.34 tff(6873,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 1.14/1.34 tff(6874,plain,
% 1.14/1.34 (~r(s(s(s(s(z)))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6549, 543, 6011, 95, 170])).
% 1.14/1.34 tff(6875,plain,
% 1.14/1.34 (b(s(s(s(s(z)))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[5892, 6874, 5968])).
% 1.14/1.34 tff(6876,plain,
% 1.14/1.34 (~r(s(z), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[4998, 543, 95, 170, 6193])).
% 1.14/1.34 tff(6877,plain,
% 1.14/1.34 (b(s(z), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[193, 6876, 5773])).
% 1.14/1.34 tff(6878,plain,
% 1.14/1.34 (~b(s(s(s(s(z)))), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6121, 206, 6877, 6875])).
% 1.14/1.34 tff(6879,plain,
% 1.14/1.34 (r(s(s(s(s(z)))), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[5878, 150, 1050, 6878])).
% 1.14/1.34 tff(6880,plain,
% 1.14/1.34 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(s(s(s(elem!1))))), elem!1))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[5988])).
% 1.14/1.34 tff(6881,assumption,(~r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 1.14/1.34 tff(6882,plain,
% 1.14/1.34 (~r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[6881, 6880])).
% 1.14/1.34 tff(6883,plain,
% 1.14/1.34 (~b(s(elem!1), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[4002, 2517, 95])).
% 1.14/1.34 tff(6884,plain,
% 1.14/1.34 (r(s(elem!1), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[1652, 6883, 99])).
% 1.14/1.34 tff(6885,plain,
% 1.14/1.34 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6129, 180, 6884, 1119])).
% 1.14/1.34 tff(6886,plain,
% 1.14/1.34 (b(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[5905, 150, 5831, 6885])).
% 1.14/1.34 tff(6887,plain,
% 1.14/1.34 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6561, 180, 781, 1119])).
% 1.14/1.34 tff(6888,plain,
% 1.14/1.34 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2753, 150, 2750, 6887])).
% 1.14/1.34 tff(6889,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(6890,plain,
% 1.14/1.34 (((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(6891,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[6890])).
% 1.14/1.34 tff(6892,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[6891, 6889])).
% 1.14/1.34 tff(6893,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(elem!1), s(s(elem!1)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(6894,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), s(z)))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[6893, 6892])).
% 1.14/1.34 tff(6895,plain,
% 1.14/1.34 (~r(s(elem!1), s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6894, 180, 781, 6884])).
% 1.14/1.34 tff(6896,plain,
% 1.14/1.34 (b(s(elem!1), s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[692, 6895, 6873])).
% 1.14/1.34 tff(6897,plain,
% 1.14/1.34 (b(s(s(elem!1)), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[267, 150, 6881, 4543])).
% 1.14/1.34 tff(6898,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(6899,plain,
% 1.14/1.34 (((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(6900,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[6899])).
% 1.14/1.34 tff(6901,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z)))))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[6900, 6898])).
% 1.14/1.34 tff(6902,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(z)))))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(6903,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(z)))))) | (~b(s(s(elem!1)), s(s(s(s(z))))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[6902, 6901])).
% 1.14/1.34 tff(6904,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6903, 206, 6897, 6896, 6888, 6886])).
% 1.14/1.34 tff(6905,plain,((~r(s(s(elem!1)), s(z))) | (s(elem!1) = s(s(s(s(z))))) | r(s(s(elem!1)), elem!1) | (s(s(elem!1)) = elem!1) | (s(s(elem!1)) = s(s(s(s(z))))) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (s(elem!1) = s(z)) | (~b(s(elem!1), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6906,plain,
% 1.14/1.34 (~r(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6905, 6881, 6011, 4543, 6012, 6873, 1119, 6193, 95, 241])).
% 1.14/1.34 tff(6907,plain,
% 1.14/1.34 (b(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[778, 6906])).
% 1.14/1.34 tff(6908,plain,
% 1.14/1.34 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[759, 6907, 735])).
% 1.14/1.34 tff(6909,plain,
% 1.14/1.34 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6167, 6908, 2883])).
% 1.14/1.34 tff(6910,plain,
% 1.14/1.34 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2377, 6909, 3061])).
% 1.14/1.34 tff(6911,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6910, 6882])).
% 1.14/1.34 tff(6912,plain,(r(s(s(elem!1)), elem!1) | (s(s(s(s(s(elem!1))))) = elem!1) | (~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = elem!1) | (s(elem!1) = s(s(elem!1))) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(elem!1), z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6913,plain,
% 1.14/1.34 (r(s(s(elem!1)), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6912, 6879, 2883, 735, 4543, 6873, 3061, 95, 6871])).
% 1.14/1.34 tff(6914,plain,
% 1.14/1.34 (~r(z, s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[813, 180, 170, 543])).
% 1.14/1.34 tff(6915,plain,
% 1.14/1.34 (b(z, s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[817, 150, 6914, 235])).
% 1.14/1.34 tff(6916,plain,
% 1.14/1.34 (~b(z, s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6656, 206, 195, 6915])).
% 1.14/1.34 tff(6917,plain,
% 1.14/1.34 (r(z, s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2185, 6916])).
% 1.14/1.34 tff(6918,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[4570, 180, 543, 6917, 6913])).
% 1.14/1.34 tff(6919,plain,((~r(z, elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (~b(s(s(s(elem!1))), s(z))) | (s(s(elem!1)) = elem!1) | (s(elem!1) = s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6920,plain,
% 1.14/1.34 (~r(z, elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6919, 735, 2883, 4543, 6873, 3061, 95, 195, 170])).
% 1.14/1.34 tff(6921,plain,
% 1.14/1.34 (b(z, elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[556, 6920, 6194])).
% 1.14/1.34 tff(6922,plain,
% 1.14/1.34 (~b(s(z), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6490, 796, 95])).
% 1.14/1.34 tff(6923,plain,
% 1.14/1.34 (r(s(z), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[467, 6922, 59])).
% 1.14/1.34 tff(6924,plain,
% 1.14/1.34 (~b(s(z), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[805, 796, 797])).
% 1.14/1.34 tff(6925,plain,
% 1.14/1.34 (r(s(z), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[193, 6924, 156])).
% 1.14/1.34 tff(6926,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[188, 6925, 6923, 170])).
% 1.14/1.34 tff(6927,plain,((~b(s(z), z)) | (~r(s(elem!1), elem!1)) | (s(z) = elem!1) | (s(z) = s(elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6928,plain,
% 1.14/1.34 (~b(s(z), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6927, 6921, 5773, 6209, 170, 95])).
% 1.14/1.34 tff(6929,plain,
% 1.14/1.34 (r(s(z), z)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[794, 6928])).
% 1.14/1.34 tff(6930,plain,
% 1.14/1.34 (~r(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[789, 6929, 6871])).
% 1.14/1.34 tff(6931,plain,
% 1.14/1.34 (b(s(s(elem!1)), s(z))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[778, 6930])).
% 1.14/1.34 tff(6932,plain,
% 1.14/1.34 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[759, 6931, 735])).
% 1.14/1.34 tff(6933,plain,
% 1.14/1.34 (~b(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6167, 6932, 2883])).
% 1.14/1.34 tff(6934,plain,
% 1.14/1.34 (r(s(s(s(s(s(elem!1))))), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2377, 6933, 3061])).
% 1.14/1.34 tff(6935,plain,
% 1.14/1.34 (r(s(s(elem!1)), elem!1)),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[6934, 5989])).
% 1.14/1.34 tff(6936,plain,
% 1.14/1.34 (~b(s(z), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[615, 6931, 195])).
% 1.14/1.34 tff(6937,plain,
% 1.14/1.34 (r(s(z), s(elem!1))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[467, 6936, 6209])).
% 1.14/1.34 tff(6938,plain,
% 1.14/1.34 (~r(s(z), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[188, 6937, 170])).
% 1.14/1.34 tff(6939,plain,
% 1.14/1.34 (b(s(z), elem!1)),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[193, 6938, 5773])).
% 1.14/1.34 tff(6940,plain,
% 1.14/1.34 (~r(s(elem!1), s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[3208, 180, 170, 6935])).
% 1.14/1.34 tff(6941,plain,
% 1.14/1.34 (b(s(elem!1), s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[692, 6940, 6873])).
% 1.14/1.34 tff(6942,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(6943,plain,
% 1.14/1.34 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(6944,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1))))))),
% 1.14/1.34 inference(monotonicity,[status(thm)],[6943])).
% 1.14/1.34 tff(6945,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))))),
% 1.14/1.34 inference(transitivity,[status(thm)],[6944, 6942])).
% 1.14/1.34 tff(6946,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 1.14/1.34 inference(quant_inst,[status(thm)],[])).
% 1.14/1.34 tff(6947,plain,
% 1.14/1.34 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1))))),
% 1.14/1.34 inference(modus_ponens,[status(thm)],[6946, 6945])).
% 1.14/1.34 tff(6948,plain,
% 1.14/1.34 ($false),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6947, 206, 95, 3211, 6519])).
% 1.14/1.34 tff(6949,plain,((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.34 tff(6950,plain,
% 1.14/1.34 (~b(z, s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[6949, 6941, 95])).
% 1.14/1.34 tff(6951,plain,
% 1.14/1.34 (r(z, s(s(elem!1)))),
% 1.14/1.34 inference(unit_resolution,[status(thm)],[2185, 6950])).
% 1.14/1.34 tff(6952,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(6953,plain,
% 1.14/1.34 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.34 inference(rewrite,[status(thm)],[])).
% 1.14/1.34 tff(6954,plain,
% 1.14/1.34 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[6953])).
% 1.14/1.35 tff(6955,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[6954, 6952])).
% 1.14/1.35 tff(6956,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(6957,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[6956, 6955])).
% 1.14/1.35 tff(6958,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[6957, 180, 3170, 6456, 6123, 2741])).
% 1.14/1.35 tff(6959,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(z, s(s(elem!1)))) | (~b(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(6960,plain,
% 1.14/1.35 (~b(s(s(s(s(z)))), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[6959, 6951, 6921, 6939])).
% 1.14/1.35 tff(6961,plain,
% 1.14/1.35 (r(s(s(s(s(z)))), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[5892, 6960, 5968])).
% 1.14/1.35 tff(6962,plain,
% 1.14/1.35 (~r(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[5866, 180, 6961, 6935])).
% 1.14/1.35 tff(6963,plain,
% 1.14/1.35 (b(s(s(elem!1)), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[2753, 150, 6012, 6962])).
% 1.14/1.35 tff(6964,plain,
% 1.14/1.35 (~r(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[6474, 180, 170, 6961])).
% 1.14/1.35 tff(6965,plain,
% 1.14/1.35 (b(s(elem!1), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[5905, 150, 6011, 6964])).
% 1.14/1.35 tff(6966,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[6724, 206, 195, 6965, 6963])).
% 1.14/1.35 tff(6967,plain,((~b(s(s(s(elem!1))), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(elem!1))) | (s(s(s(s(s(elem!1))))) = elem!1) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(6968,plain,
% 1.14/1.35 (~b(s(s(s(elem!1))), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[6967, 170, 195, 95, 6684, 3061, 2883, 4543])).
% 1.14/1.35 tff(6969,plain,
% 1.14/1.35 (~b(elem!1, s(z))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[6968, 6872])).
% 1.14/1.35 tff(6970,plain,
% 1.14/1.35 (r(elem!1, s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[154, 6969, 6574])).
% 1.14/1.35 tff(6971,plain,
% 1.14/1.35 (~r(s(elem!1), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[3897, 6970, 170])).
% 1.14/1.35 tff(6972,plain,
% 1.14/1.35 (b(s(elem!1), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1652, 6971, 6193])).
% 1.14/1.35 tff(6973,plain,
% 1.14/1.35 (~b(s(z), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[4002, 6972, 95])).
% 1.14/1.35 tff(6974,plain,
% 1.14/1.35 (r(s(z), z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[794, 6973])).
% 1.14/1.35 tff(6975,plain,
% 1.14/1.35 (~r(s(s(elem!1)), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[789, 6974, 6871])).
% 1.14/1.35 tff(6976,plain,
% 1.14/1.35 (~b(elem!1, s(elem!1))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[6403, 6970, 95, 6193, 170])).
% 1.14/1.35 tff(6977,plain,
% 1.14/1.35 (r(elem!1, s(elem!1))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[401, 6976, 54])).
% 1.14/1.35 tff(6978,plain,
% 1.14/1.35 (~r(s(z), s(elem!1))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[450, 6977, 6970])).
% 1.14/1.35 tff(6979,plain,
% 1.14/1.35 (b(s(z), s(elem!1))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[467, 6978, 6209])).
% 1.14/1.35 tff(6980,plain,
% 1.14/1.35 (~b(s(s(elem!1)), s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[615, 6979, 195])).
% 1.14/1.35 tff(6981,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[778, 6980, 6975])).
% 1.14/1.35 tff(6982,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (elem!1 = s(elem!1)) | (~(s(s(s(elem!1))) = elem!1)) | (s(s(s(s(s(elem!1))))) = elem!1) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(6983,plain,
% 1.14/1.35 (~r(s(elem!1), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[6982, 6565, 6866, 46, 5757, 5791, 30])).
% 1.14/1.35 tff(6984,plain,
% 1.14/1.35 (b(s(elem!1), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[167, 6983, 38])).
% 1.14/1.35 tff(6985,plain,
% 1.14/1.35 (~b(elem!1, z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[4492, 6984, 6866])).
% 1.14/1.35 tff(6986,plain,
% 1.14/1.35 (r(elem!1, z)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[387, 6985, 6869])).
% 1.14/1.35 tff(6987,plain,
% 1.14/1.35 (~r(s(s(elem!1)), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[4794, 180, 6986, 6868])).
% 1.14/1.35 tff(6988,plain,
% 1.14/1.35 (~b(s(s(elem!1)), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[6758, 6984, 6565])).
% 1.14/1.35 tff(6989,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[267, 150, 6988, 6987, 30])).
% 1.14/1.35 tff(6990,plain,(s(s(s(elem!1))) = s(elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(6991,plain,
% 1.14/1.35 (inj_0(s(s(s(elem!1)))) = inj_0(s(elem!1))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[6990])).
% 1.14/1.35 tff(6992,plain,
% 1.14/1.35 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[6990])).
% 1.14/1.35 tff(6993,plain,
% 1.14/1.35 (s(s(s(s(elem!1)))) = elem!1),
% 1.14/1.35 inference(transitivity,[status(thm)],[6992, 72, 6991, 10])).
% 1.14/1.35 tff(6994,plain,
% 1.14/1.35 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[6993])).
% 1.14/1.35 tff(6995,plain,
% 1.14/1.35 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[6994])).
% 1.14/1.35 tff(6996,plain,
% 1.14/1.35 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 1.14/1.35 inference(transitivity,[status(thm)],[6995, 72, 6991, 10])).
% 1.14/1.35 tff(6997,plain,
% 1.14/1.35 (b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(z))), elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[6996])).
% 1.14/1.35 tff(6998,plain,
% 1.14/1.35 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(s(s(z)))), elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[6996])).
% 1.14/1.35 tff(6999,plain,
% 1.14/1.35 (r(s(s(s(s(z)))), elem!1) <=> r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(symmetry,[status(thm)],[6998])).
% 1.14/1.35 tff(7000,plain,
% 1.14/1.35 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[5860, 6999])).
% 1.14/1.35 tff(7001,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7002,plain,
% 1.14/1.35 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7003,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[7002])).
% 1.14/1.35 tff(7004,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[7003, 7001])).
% 1.14/1.35 tff(7005,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(7006,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[7005, 7004])).
% 1.14/1.35 tff(7007,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7006, 206, 2728, 3555, 1263])).
% 1.14/1.35 tff(7008,plain,((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(7009,plain,
% 1.14/1.35 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7008, 3555, 2728])).
% 1.14/1.35 tff(7010,assumption,(s(s(s(s(z)))) = s(s(z))), introduced(assumption)).
% 1.14/1.35 tff(7011,plain,
% 1.14/1.35 (inj_0(s(s(s(s(z))))) = inj_0(s(s(z)))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[7010])).
% 1.14/1.35 tff(7012,plain,
% 1.14/1.35 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.35 inference(symmetry,[status(thm)],[7011])).
% 1.14/1.35 tff(7013,plain,
% 1.14/1.35 (s(z) = s(s(s(z)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[1332, 7012, 1030])).
% 1.14/1.35 tff(7014,plain,
% 1.14/1.35 (inj_0(s(z)) = inj_0(s(s(s(z))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[7013])).
% 1.14/1.35 tff(7015,plain,
% 1.14/1.35 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.14/1.35 inference(symmetry,[status(thm)],[7014])).
% 1.14/1.35 tff(7016,plain,
% 1.14/1.35 (s(s(z)) = z),
% 1.14/1.35 inference(transitivity,[status(thm)],[1036, 7015, 106])).
% 1.14/1.35 tff(7017,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1951, 7016])).
% 1.14/1.35 tff(7018,plain,(~(s(s(s(s(z)))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(7019,assumption,(~b(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.14/1.35 tff(7020,assumption,(~r(s(s(s(s(z)))), s(s(z)))), introduced(assumption)).
% 1.14/1.35 tff(7021,plain,
% 1.14/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7022,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(7023,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(z))) | b(s(s(s(s(z)))), s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[7022, 7021])).
% 1.14/1.35 tff(7024,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7023, 150, 7020, 7019, 7018])).
% 1.14/1.35 tff(7025,plain,(r(s(s(s(s(z)))), s(s(z))) | b(s(s(s(s(z)))), s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(7026,plain,
% 1.14/1.35 (r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7025, 7009])).
% 1.14/1.35 tff(7027,plain,
% 1.14/1.35 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(s(s(z)))), elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[6996])).
% 1.14/1.35 tff(7028,plain,
% 1.14/1.35 (b(s(s(s(s(z)))), elem!1) <=> b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(symmetry,[status(thm)],[7027])).
% 1.14/1.35 tff(7029,plain,
% 1.14/1.35 (b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[2728, 7028])).
% 1.14/1.35 tff(7030,plain,
% 1.14/1.35 (b(s(s(z)), s(s(s(s(s(s(elem!1))))))) <=> b(s(s(z)), elem!1)),
% 1.14/1.35 inference(monotonicity,[status(thm)],[6996])).
% 1.14/1.35 tff(7031,plain,
% 1.14/1.35 (b(s(s(z)), elem!1) <=> b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(symmetry,[status(thm)],[7030])).
% 1.14/1.35 tff(7032,plain,
% 1.14/1.35 (b(s(s(z)), s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[3555, 7031])).
% 1.14/1.35 tff(7033,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7034,plain,
% 1.14/1.35 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7035,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[7034])).
% 1.14/1.35 tff(7036,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[7035, 7033])).
% 1.14/1.35 tff(7037,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), s(s(s(s(z)))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(7038,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[7037, 7036])).
% 1.14/1.35 tff(7039,plain,
% 1.14/1.35 (~b(s(z), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7038, 206, 117, 2728])).
% 1.14/1.35 tff(7040,plain,
% 1.14/1.35 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 1.14/1.35 inference(commutativity,[status(thm)],[])).
% 1.14/1.35 tff(7041,plain,
% 1.14/1.35 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 1.14/1.35 inference(symmetry,[status(thm)],[7040])).
% 1.14/1.35 tff(7042,plain,
% 1.14/1.35 ((~(s(s(s(s(z)))) = s(z))) <=> (~(s(z) = s(s(s(s(z))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[7041])).
% 1.14/1.35 tff(7043,plain,
% 1.14/1.35 (~(s(z) = s(s(s(s(z)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1050, 7042])).
% 1.14/1.35 tff(7044,plain,
% 1.14/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7045,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z))))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(7046,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[7045, 7044])).
% 1.14/1.35 tff(7047,plain,
% 1.14/1.35 ((s(z) = s(s(s(s(z))))) | b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7046, 150])).
% 1.14/1.35 tff(7048,plain,
% 1.14/1.35 (b(s(z), s(s(s(s(z))))) | r(s(z), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7047, 7043])).
% 1.14/1.35 tff(7049,plain,
% 1.14/1.35 (r(s(z), s(s(s(s(z)))))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7048, 7039])).
% 1.14/1.35 tff(7050,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7051,plain,
% 1.14/1.35 (((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7052,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[7051])).
% 1.14/1.35 tff(7053,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[7052, 7050])).
% 1.14/1.35 tff(7054,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(7055,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[7054, 7053])).
% 1.14/1.35 tff(7056,plain,
% 1.14/1.35 (~b(s(z), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7055, 206, 117, 3555])).
% 1.14/1.35 tff(7057,plain,
% 1.14/1.35 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 1.14/1.35 inference(commutativity,[status(thm)],[])).
% 1.14/1.35 tff(7058,plain,
% 1.14/1.35 ((~(s(s(z)) = s(z))) <=> (~(s(z) = s(s(z))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[7057])).
% 1.14/1.35 tff(7059,assumption,(s(s(z)) = s(z)), introduced(assumption)).
% 1.14/1.35 tff(7060,plain,
% 1.14/1.35 (s(z) = s(s(z))),
% 1.14/1.35 inference(symmetry,[status(thm)],[7059])).
% 1.14/1.35 tff(7061,plain,
% 1.14/1.35 (inj_0(s(z)) = inj_0(s(s(z)))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[7060])).
% 1.14/1.35 tff(7062,plain,
% 1.14/1.35 (inj_0(s(s(z))) = inj_0(s(z))),
% 1.14/1.35 inference(symmetry,[status(thm)],[7061])).
% 1.14/1.35 tff(7063,plain,
% 1.14/1.35 (s(z) = z),
% 1.14/1.35 inference(transitivity,[status(thm)],[1332, 7062, 106])).
% 1.14/1.35 tff(7064,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[499, 7063])).
% 1.14/1.35 tff(7065,plain,(~(s(s(z)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(7066,plain,
% 1.14/1.35 (~(s(z) = s(s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[7065, 7058])).
% 1.14/1.35 tff(7067,plain,
% 1.14/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7068,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(7069,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[7068, 7067])).
% 1.14/1.35 tff(7070,plain,
% 1.14/1.35 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7069, 150])).
% 1.14/1.35 tff(7071,plain,
% 1.14/1.35 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7070, 7066])).
% 1.14/1.35 tff(7072,plain,
% 1.14/1.35 (r(s(z), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7071, 7056])).
% 1.14/1.35 tff(7073,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7074,plain,
% 1.14/1.35 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7075,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z))))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[7074])).
% 1.14/1.35 tff(7076,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z)))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[7075, 7073])).
% 1.14/1.35 tff(7077,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(7078,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(z), s(s(s(s(z))))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[7077, 7076])).
% 1.14/1.35 tff(7079,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7078, 180, 7026, 7072, 1119, 7049])).
% 1.14/1.35 tff(7080,plain,((~b(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(7081,plain,
% 1.14/1.35 (~b(s(z), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7080, 1119, 3555, 2728])).
% 1.14/1.35 tff(7082,plain,
% 1.14/1.35 (~(elem!1 = s(z))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[1288, 6990])).
% 1.14/1.35 tff(7083,plain,
% 1.14/1.35 (~(s(z) = elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[4953, 7082])).
% 1.14/1.35 tff(7084,plain,
% 1.14/1.35 (b(s(z), elem!1) | r(s(z), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[193, 7083])).
% 1.14/1.35 tff(7085,plain,
% 1.14/1.35 (r(s(z), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7084, 7081])).
% 1.14/1.35 tff(7086,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7087,plain,
% 1.14/1.35 (((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7088,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[7087])).
% 1.14/1.35 tff(7089,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[7088, 7086])).
% 1.14/1.35 tff(7090,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z)))))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(7091,plain,
% 1.14/1.35 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), s(s(z))))),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[7090, 7089])).
% 1.14/1.35 tff(7092,plain,
% 1.14/1.35 ($false),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7091, 180, 169, 3017, 2270])).
% 1.14/1.35 tff(7093,plain,((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.35 tff(7094,plain,
% 1.14/1.35 (~r(s(s(z)), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7093, 2270, 169])).
% 1.14/1.35 tff(7095,plain,
% 1.14/1.35 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 1.14/1.35 inference(symmetry,[status(thm)],[6995])).
% 1.14/1.35 tff(7096,plain,
% 1.14/1.35 (inj_0(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 1.14/1.35 inference(symmetry,[status(thm)],[6991])).
% 1.14/1.35 tff(7097,plain,
% 1.14/1.35 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 1.14/1.35 inference(transitivity,[status(thm)],[52, 7096, 71, 7095])).
% 1.14/1.35 tff(7098,plain,
% 1.14/1.35 ((s(s(z)) = elem!1) <=> (s(s(z)) = s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[7097])).
% 1.14/1.35 tff(7099,plain,
% 1.14/1.35 ((s(s(z)) = elem!1) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(z)))),
% 1.14/1.35 inference(transitivity,[status(thm)],[7098, 1091])).
% 1.14/1.35 tff(7100,plain,
% 1.14/1.35 ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) <=> (s(s(z)) = elem!1)),
% 1.14/1.35 inference(symmetry,[status(thm)],[7099])).
% 1.14/1.35 tff(7101,plain,
% 1.14/1.35 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(z)))) <=> (~(s(s(z)) = elem!1))),
% 1.14/1.35 inference(monotonicity,[status(thm)],[7100])).
% 1.14/1.35 tff(7102,plain,
% 1.14/1.35 (~(s(s(z)) = elem!1)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[1111, 7101])).
% 1.14/1.35 tff(7103,plain,
% 1.14/1.35 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7104,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1))),
% 1.14/1.35 inference(quant_inst,[status(thm)],[])).
% 1.14/1.35 tff(7105,plain,
% 1.14/1.35 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.14/1.35 inference(modus_ponens,[status(thm)],[7104, 7103])).
% 1.14/1.35 tff(7106,plain,
% 1.14/1.35 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7105, 150])).
% 1.14/1.35 tff(7107,plain,
% 1.14/1.35 (b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7106, 7102])).
% 1.14/1.35 tff(7108,plain,
% 1.14/1.35 (b(s(s(z)), elem!1)),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7107, 7094])).
% 1.14/1.35 tff(7109,plain,
% 1.14/1.35 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7006, 206, 2728, 7108])).
% 1.14/1.35 tff(7110,plain,
% 1.14/1.35 (r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.35 inference(unit_resolution,[status(thm)],[7023, 150, 7109, 7018])).
% 1.14/1.35 tff(7111,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7112,plain,
% 1.14/1.35 (((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.35 inference(rewrite,[status(thm)],[])).
% 1.14/1.35 tff(7113,plain,
% 1.14/1.35 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[7112])).
% 1.14/1.36 tff(7114,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[7113, 7111])).
% 1.14/1.36 tff(7115,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(7116,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(s(z)))), s(z)))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[7115, 7114])).
% 1.14/1.36 tff(7117,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7116, 180, 169, 7110, 2270, 1119])).
% 1.14/1.36 tff(7118,plain,((~r(s(z), s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(7119,plain,
% 1.14/1.36 (~r(s(z), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7118, 7085, 1119, 2728])).
% 1.14/1.36 tff(7120,plain,
% 1.14/1.36 (b(s(z), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7071, 7119])).
% 1.14/1.36 tff(7121,plain,
% 1.14/1.36 (b(s(s(s(z))), elem!1) <=> b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[6997])).
% 1.14/1.36 tff(7122,plain,
% 1.14/1.36 ((~b(s(s(s(z))), elem!1)) <=> (~b(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[7121])).
% 1.14/1.36 tff(7123,plain,
% 1.14/1.36 (~r(z, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[4723, 180, 485, 2042])).
% 1.14/1.36 tff(7124,plain,
% 1.14/1.36 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 1.14/1.36 inference(commutativity,[status(thm)],[])).
% 1.14/1.36 tff(7125,plain,
% 1.14/1.36 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[7124])).
% 1.14/1.36 tff(7126,plain,
% 1.14/1.36 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[7125])).
% 1.14/1.36 tff(7127,plain,
% 1.14/1.36 (~(z = s(s(s(z))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[1048, 7126])).
% 1.14/1.36 tff(7128,plain,
% 1.14/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7129,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(7130,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[7129, 7128])).
% 1.14/1.36 tff(7131,plain,
% 1.14/1.36 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7130, 150])).
% 1.14/1.36 tff(7132,plain,
% 1.14/1.36 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7131, 7127])).
% 1.14/1.36 tff(7133,plain,
% 1.14/1.36 (b(z, s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7132, 7123])).
% 1.14/1.36 tff(7134,plain,
% 1.14/1.36 (~r(s(s(z)), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2150, 1422, 485])).
% 1.14/1.36 tff(7135,assumption,(~r(s(s(z)), z)), introduced(assumption)).
% 1.14/1.36 tff(7136,plain,
% 1.14/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7137,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(7138,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = z) | b(s(s(z)), z) | r(s(s(z)), z)),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[7137, 7136])).
% 1.14/1.36 tff(7139,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7138, 150, 1951, 7135, 2492])).
% 1.14/1.36 tff(7140,plain,(b(s(s(z)), z) | r(s(s(z)), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(7141,plain,
% 1.14/1.36 (b(s(s(z)), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7140, 7134])).
% 1.14/1.36 tff(7142,plain,
% 1.14/1.36 (~r(s(s(z)), s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2619, 180, 2042, 1422])).
% 1.14/1.36 tff(7143,plain,
% 1.14/1.36 (s(z) = s(s(z))),
% 1.14/1.36 inference(transitivity,[status(thm)],[1332, 3511, 1035])).
% 1.14/1.36 tff(7144,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7066, 7143])).
% 1.14/1.36 tff(7145,plain,(~(s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(7146,plain,
% 1.14/1.36 (~(s(s(z)) = s(s(s(z))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[7145, 3508])).
% 1.14/1.36 tff(7147,plain,
% 1.14/1.36 ((s(s(z)) = s(s(s(z)))) | b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[3552, 150])).
% 1.14/1.36 tff(7148,plain,
% 1.14/1.36 (b(s(s(z)), s(s(s(z)))) | r(s(s(z)), s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7147, 7146])).
% 1.14/1.36 tff(7149,plain,
% 1.14/1.36 (b(s(s(z)), s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7148, 7142])).
% 1.14/1.36 tff(7150,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7151,plain,
% 1.14/1.36 (((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7152,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[7151])).
% 1.14/1.36 tff(7153,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[7152, 7150])).
% 1.14/1.36 tff(7154,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(7155,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[7154, 7153])).
% 1.14/1.36 tff(7156,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7155, 206, 7149, 7141, 7133])).
% 1.14/1.36 tff(7157,plain,((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(7158,plain,
% 1.14/1.36 (~r(s(s(s(z))), s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7157, 1422, 485])).
% 1.14/1.36 tff(7159,plain,
% 1.14/1.36 (inj_0(s(s(s(z)))) = inj_0(s(z))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[1717])).
% 1.14/1.36 tff(7160,plain,
% 1.14/1.36 (s(s(z)) = z),
% 1.14/1.36 inference(transitivity,[status(thm)],[1036, 7159, 106])).
% 1.14/1.36 tff(7161,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1951, 7160])).
% 1.14/1.36 tff(7162,plain,(~(s(s(s(z))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(7163,plain,
% 1.14/1.36 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1865, 7162])).
% 1.14/1.36 tff(7164,plain,
% 1.14/1.36 (b(s(s(s(z))), s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7163, 7158])).
% 1.14/1.36 tff(7165,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[3670, 180, 543, 441, 485])).
% 1.14/1.36 tff(7166,plain,((~r(elem!1, s(z))) | (~r(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(7167,plain,
% 1.14/1.36 (~r(elem!1, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7166, 543, 485])).
% 1.14/1.36 tff(7168,plain,
% 1.14/1.36 (b(elem!1, s(z)) | r(elem!1, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[154, 7082])).
% 1.14/1.36 tff(7169,plain,
% 1.14/1.36 (b(elem!1, s(z))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7168, 7167])).
% 1.14/1.36 tff(7170,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7171,plain,
% 1.14/1.36 (((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))) <=> ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7172,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[7171])).
% 1.14/1.36 tff(7173,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[7172, 7170])).
% 1.14/1.36 tff(7174,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(7175,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(z)), s(z))) | (~r(z, s(s(z))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[7174, 7173])).
% 1.14/1.36 tff(7176,plain,
% 1.14/1.36 (~r(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7175, 180, 485, 1422])).
% 1.14/1.36 tff(7177,plain,
% 1.14/1.36 ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2013, 150])).
% 1.14/1.36 tff(7178,plain,
% 1.14/1.36 (b(z, s(s(z))) | r(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7177, 1952])).
% 1.14/1.36 tff(7179,plain,
% 1.14/1.36 (b(z, s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7178, 7176])).
% 1.14/1.36 tff(7180,plain,
% 1.14/1.36 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 1.14/1.36 inference(commutativity,[status(thm)],[])).
% 1.14/1.36 tff(7181,plain,
% 1.14/1.36 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[7180])).
% 1.14/1.36 tff(7182,plain,
% 1.14/1.36 ((~(s(s(s(s(z)))) = s(s(z)))) <=> (~(s(s(z)) = s(s(s(s(z))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[7181])).
% 1.14/1.36 tff(7183,plain,
% 1.14/1.36 (~(s(s(z)) = s(s(s(s(z)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[7018, 7182])).
% 1.14/1.36 tff(7184,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7185,plain,
% 1.14/1.36 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7186,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[7185])).
% 1.14/1.36 tff(7187,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[7186, 7184])).
% 1.14/1.36 tff(7188,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(7189,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[7188, 7187])).
% 1.14/1.36 tff(7190,plain,
% 1.14/1.36 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7189, 206, 2200, 7141])).
% 1.14/1.36 tff(7191,plain,
% 1.14/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7192,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z))))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(7193,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(s(s(z))))) | b(s(s(z)), s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[7192, 7191])).
% 1.14/1.36 tff(7194,plain,
% 1.14/1.36 ((s(s(z)) = s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7193, 150, 7190])).
% 1.14/1.36 tff(7195,plain,
% 1.14/1.36 (r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7194, 7183])).
% 1.14/1.36 tff(7196,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7197,plain,
% 1.14/1.36 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7198,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[7197])).
% 1.14/1.36 tff(7199,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[7198, 7196])).
% 1.14/1.36 tff(7200,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(7201,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[7200, 7199])).
% 1.14/1.36 tff(7202,plain,
% 1.14/1.36 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7201, 206, 7164, 2200, 4730])).
% 1.14/1.36 tff(7203,plain,
% 1.14/1.36 (s(s(s(z))) = s(s(s(s(z))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[1271])).
% 1.14/1.36 tff(7204,plain,
% 1.14/1.36 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[7203])).
% 1.14/1.36 tff(7205,plain,
% 1.14/1.36 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(z))))),
% 1.14/1.36 inference(symmetry,[status(thm)],[7204])).
% 1.14/1.36 tff(7206,plain,
% 1.14/1.36 (s(s(s(z))) = s(s(z))),
% 1.14/1.36 inference(transitivity,[status(thm)],[1031, 7205, 1035])).
% 1.14/1.36 tff(7207,plain,
% 1.14/1.36 ($false),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1692, 7206])).
% 1.14/1.36 tff(7208,plain,((~(s(s(s(s(z)))) = s(s(s(z))))) | (s(s(s(z))) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.36 tff(7209,plain,
% 1.14/1.36 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7208, 7145])).
% 1.14/1.36 tff(7210,plain,
% 1.14/1.36 (~(s(s(s(z))) = s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2467, 7209])).
% 1.14/1.36 tff(7211,plain,
% 1.14/1.36 ((s(s(s(z))) = s(s(s(s(z))))) | b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[2471, 150])).
% 1.14/1.36 tff(7212,plain,
% 1.14/1.36 (b(s(s(s(z))), s(s(s(s(z))))) | r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7211, 7210])).
% 1.14/1.36 tff(7213,plain,
% 1.14/1.36 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7212, 7202])).
% 1.14/1.36 tff(7214,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7215,plain,
% 1.14/1.36 (((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7216,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[7215])).
% 1.14/1.36 tff(7217,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.36 inference(transitivity,[status(thm)],[7216, 7214])).
% 1.14/1.36 tff(7218,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(7219,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[7218, 7217])).
% 1.14/1.36 tff(7220,plain,
% 1.14/1.36 (~r(s(s(s(z))), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7219, 180, 1422, 7213, 7195])).
% 1.14/1.36 tff(7221,plain,
% 1.14/1.36 (b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[1307, 7145])).
% 1.14/1.36 tff(7222,plain,
% 1.14/1.36 (b(s(s(s(z))), s(s(z)))),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7221, 7220])).
% 1.14/1.36 tff(7223,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7224,plain,
% 1.14/1.36 (((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7225,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))))),
% 1.14/1.36 inference(monotonicity,[status(thm)],[7224])).
% 1.14/1.36 tff(7226,plain,
% 1.14/1.36 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(transitivity,[status(thm)],[7225, 7223])).
% 1.14/1.36 tff(7227,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z)))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.36 tff(7228,plain,
% 1.14/1.36 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(z))), z))),
% 1.14/1.36 inference(modus_ponens,[status(thm)],[7227, 7226])).
% 1.14/1.36 tff(7229,plain,
% 1.14/1.36 (~b(s(s(s(z))), z)),
% 1.14/1.36 inference(unit_resolution,[status(thm)],[7228, 206, 7222, 7179])).
% 1.14/1.36 tff(7230,plain,
% 1.14/1.36 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.14/1.36 inference(rewrite,[status(thm)],[])).
% 1.14/1.36 tff(7231,plain,
% 1.14/1.36 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z))),
% 1.14/1.36 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(7232,plain,
% 1.14/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = z) | b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[7231, 7230])).
% 1.14/1.37 tff(7233,plain,
% 1.14/1.37 (r(s(s(s(z))), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7232, 150, 1048, 7229])).
% 1.14/1.37 tff(7234,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2314, 206, 1263, 2200, 2496])).
% 1.14/1.37 tff(7235,plain,((~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7236,plain,
% 1.14/1.37 (~b(s(s(z)), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7235, 1263, 2200])).
% 1.14/1.37 tff(7237,plain,
% 1.14/1.37 (r(s(s(z)), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7138, 150, 1951, 7236])).
% 1.14/1.37 tff(7238,plain,
% 1.14/1.37 (~r(s(s(z)), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2150, 7237, 485])).
% 1.14/1.37 tff(7239,plain,
% 1.14/1.37 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7240,plain,
% 1.14/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(7241,plain,
% 1.14/1.37 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[7240, 7239])).
% 1.14/1.37 tff(7242,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7241, 150, 1458, 1627, 7065])).
% 1.14/1.37 tff(7243,plain,(b(s(s(z)), s(z)) | r(s(s(z)), s(z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7244,plain,
% 1.14/1.37 (b(s(s(z)), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7243, 7238])).
% 1.14/1.37 tff(7245,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7246,plain,
% 1.14/1.37 (((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7247,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7246])).
% 1.14/1.37 tff(7248,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[7247, 7245])).
% 1.14/1.37 tff(7249,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(7250,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[7249, 7248])).
% 1.14/1.37 tff(7251,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7250, 206, 7244, 1263, 4730])).
% 1.14/1.37 tff(7252,plain,((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7253,plain,
% 1.14/1.37 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7252, 2200, 485, 4730])).
% 1.14/1.37 tff(7254,plain,
% 1.14/1.37 (r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7025, 7253])).
% 1.14/1.37 tff(7255,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7256,plain,
% 1.14/1.37 (((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7257,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7256])).
% 1.14/1.37 tff(7258,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[7257, 7255])).
% 1.14/1.37 tff(7259,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(7260,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[7259, 7258])).
% 1.14/1.37 tff(7261,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7260, 180, 5860, 3017, 1691])).
% 1.14/1.37 tff(7262,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7263,plain,
% 1.14/1.37 (~r(s(s(s(s(z)))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7262, 3017, 1691])).
% 1.14/1.37 tff(7264,plain,
% 1.14/1.37 (s(s(s(s(z)))) = s(s(elem!1))),
% 1.14/1.37 inference(transitivity,[status(thm)],[5759, 52, 7096, 71])).
% 1.14/1.37 tff(7265,plain,
% 1.14/1.37 (inj_0(s(s(s(s(z))))) = inj_0(s(s(elem!1)))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7264])).
% 1.14/1.37 tff(7266,plain,
% 1.14/1.37 (s(s(s(z))) = s(elem!1)),
% 1.14/1.37 inference(transitivity,[status(thm)],[1031, 7265, 48])).
% 1.14/1.37 tff(7267,plain,
% 1.14/1.37 (inj_0(s(s(s(z)))) = inj_0(s(elem!1))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7266])).
% 1.14/1.37 tff(7268,plain,
% 1.14/1.37 (inj_0(s(elem!1)) = inj_0(s(s(s(z))))),
% 1.14/1.37 inference(symmetry,[status(thm)],[7267])).
% 1.14/1.37 tff(7269,plain,
% 1.14/1.37 (s(s(s(s(s(s(elem!1)))))) = s(s(z))),
% 1.14/1.37 inference(transitivity,[status(thm)],[6995, 72, 6991, 7268, 1035])).
% 1.14/1.37 tff(7270,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[1111, 7269])).
% 1.14/1.37 tff(7271,plain,(~(s(s(s(s(z)))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7272,plain,
% 1.14/1.37 (b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[5892, 7271])).
% 1.14/1.37 tff(7273,plain,
% 1.14/1.37 (b(s(s(s(s(z)))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7272, 7263])).
% 1.14/1.37 tff(7274,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7275,plain,
% 1.14/1.37 (((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7276,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7275])).
% 1.14/1.37 tff(7277,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[7276, 7274])).
% 1.14/1.37 tff(7278,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(7279,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[7278, 7277])).
% 1.14/1.37 tff(7280,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7279, 206, 157, 2728, 4730])).
% 1.14/1.37 tff(7281,plain,((~b(s(s(s(s(z)))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(s(z)))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7282,plain,
% 1.14/1.37 (~b(elem!1, s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7281, 7273, 4730])).
% 1.14/1.37 tff(7283,plain,
% 1.14/1.37 (r(elem!1, s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7168, 7282])).
% 1.14/1.37 tff(7284,plain,
% 1.14/1.37 (~r(z, elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7166, 7283, 485])).
% 1.14/1.37 tff(7285,plain,
% 1.14/1.37 (s(s(elem!1)) = elem!1),
% 1.14/1.37 inference(transitivity,[status(thm)],[72, 6991, 10])).
% 1.14/1.37 tff(7286,plain,
% 1.14/1.37 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7285])).
% 1.14/1.37 tff(7287,plain,
% 1.14/1.37 ((s(s(elem!1)) = z) <=> (z = elem!1)),
% 1.14/1.37 inference(transitivity,[status(thm)],[7286, 131])).
% 1.14/1.37 tff(7288,plain,
% 1.14/1.37 ((~(s(s(elem!1)) = z)) <=> (~(z = elem!1))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7287])).
% 1.14/1.37 tff(7289,plain,
% 1.14/1.37 (~(z = elem!1)),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[224, 7288])).
% 1.14/1.37 tff(7290,plain,
% 1.14/1.37 (b(z, elem!1) | r(z, elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[556, 7289])).
% 1.14/1.37 tff(7291,plain,
% 1.14/1.37 (b(z, elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7290, 7284])).
% 1.14/1.37 tff(7292,assumption,(~r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.14/1.37 tff(7293,assumption,(~b(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.14/1.37 tff(7294,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[2740, 150, 2737, 7293, 7292])).
% 1.14/1.37 tff(7295,plain,(r(s(s(s(s(z)))), z) | b(s(s(s(s(z)))), z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7296,plain,
% 1.14/1.37 (r(s(s(s(s(z)))), z)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7295, 2735])).
% 1.14/1.37 tff(7297,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7298,plain,
% 1.14/1.37 (((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7299,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7298])).
% 1.14/1.37 tff(7300,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[7299, 7297])).
% 1.14/1.37 tff(7301,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(7302,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), z))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[7301, 7300])).
% 1.14/1.37 tff(7303,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7302, 180, 6456, 6123, 7296])).
% 1.14/1.37 tff(7304,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7305,plain,
% 1.14/1.37 (~b(s(z), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7304, 7291, 7273])).
% 1.14/1.37 tff(7306,plain,
% 1.14/1.37 (r(s(z), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7084, 7305])).
% 1.14/1.37 tff(7307,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7308,plain,
% 1.14/1.37 (((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7309,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7308])).
% 1.14/1.37 tff(7310,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[7309, 7307])).
% 1.14/1.37 tff(7311,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(7312,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[7311, 7310])).
% 1.14/1.37 tff(7313,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7312, 180, 7306, 1422, 3017])).
% 1.14/1.37 tff(7314,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7315,plain,
% 1.14/1.37 (~r(s(s(z)), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7314, 1422, 485, 4730, 7254])).
% 1.14/1.37 tff(7316,plain,
% 1.14/1.37 (b(s(s(z)), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7107, 7315])).
% 1.14/1.37 tff(7317,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7318,plain,
% 1.14/1.37 (((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z))) <=> ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7319,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7318])).
% 1.14/1.37 tff(7320,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[7319, 7317])).
% 1.14/1.37 tff(7321,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(7322,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[7321, 7320])).
% 1.14/1.37 tff(7323,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7322, 206, 797, 3555, 2496])).
% 1.14/1.37 tff(7324,plain,((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7325,plain,
% 1.14/1.37 (~b(z, elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7324, 7316, 7141])).
% 1.14/1.37 tff(7326,plain,
% 1.14/1.37 (r(z, elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7290, 7325])).
% 1.14/1.37 tff(7327,plain,
% 1.14/1.37 (~r(elem!1, s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7166, 7326, 485])).
% 1.14/1.37 tff(7328,plain,
% 1.14/1.37 (b(elem!1, s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7168, 7327])).
% 1.14/1.37 tff(7329,plain,
% 1.14/1.37 (~b(s(s(s(s(z)))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7281, 7328, 4730])).
% 1.14/1.37 tff(7330,plain,
% 1.14/1.37 (r(s(s(s(s(z)))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7272, 7329])).
% 1.14/1.37 tff(7331,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7332,plain,
% 1.14/1.37 (((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7333,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7332])).
% 1.14/1.37 tff(7334,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 1.14/1.37 inference(transitivity,[status(thm)],[7333, 7331])).
% 1.14/1.37 tff(7335,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(7336,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[7335, 7334])).
% 1.14/1.37 tff(7337,plain,
% 1.14/1.37 (~r(z, s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7336, 180, 169, 543])).
% 1.14/1.37 tff(7338,plain,
% 1.14/1.37 (b(z, s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[505, 7337])).
% 1.14/1.37 tff(7339,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[6109, 206, 7338, 6541, 5879])).
% 1.14/1.37 tff(7340,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7341,plain,
% 1.14/1.37 (~r(s(s(s(s(z)))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7340, 543, 169])).
% 1.14/1.37 tff(7342,plain,
% 1.14/1.37 (b(s(s(s(s(z)))), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7272, 7341])).
% 1.14/1.37 tff(7343,plain,
% 1.14/1.37 (~b(s(s(s(s(z)))), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7281, 157, 7342])).
% 1.14/1.37 tff(7344,plain,
% 1.14/1.37 (b(s(s(s(s(z)))), s(z)) | r(s(s(s(s(z)))), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[5878, 150, 1050])).
% 1.14/1.37 tff(7345,plain,
% 1.14/1.37 (r(s(s(s(s(z)))), s(z))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7344, 7343])).
% 1.14/1.37 tff(7346,plain,
% 1.14/1.37 (~r(s(z), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7118, 7345, 169, 7342])).
% 1.14/1.37 tff(7347,plain,
% 1.14/1.37 (b(s(z), s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7070, 7346, 7066])).
% 1.14/1.37 tff(7348,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 1.14/1.37 tff(7349,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7350,plain,
% 1.14/1.37 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7351,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7350])).
% 1.14/1.37 tff(7352,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[7351, 7349])).
% 1.14/1.37 tff(7353,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(7354,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[7353, 7352])).
% 1.14/1.37 tff(7355,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7354, 206, 911, 1250, 7348])).
% 1.14/1.37 tff(7356,plain,((~b(s(z), s(s(z)))) | (~b(z, s(z))) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7357,plain,
% 1.14/1.37 (~b(z, s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7356, 7347, 7338])).
% 1.14/1.37 tff(7358,plain,
% 1.14/1.37 (r(z, s(s(z)))),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7178, 7357])).
% 1.14/1.37 tff(7359,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 1.14/1.37 tff(7360,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7361,plain,
% 1.14/1.37 (((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))) <=> ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.14/1.37 inference(rewrite,[status(thm)],[])).
% 1.14/1.37 tff(7362,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))))),
% 1.14/1.37 inference(monotonicity,[status(thm)],[7361])).
% 1.14/1.37 tff(7363,plain,
% 1.14/1.37 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.14/1.37 inference(transitivity,[status(thm)],[7362, 7360])).
% 1.14/1.37 tff(7364,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 1.14/1.37 inference(quant_inst,[status(thm)],[])).
% 1.14/1.37 tff(7365,plain,
% 1.14/1.37 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))),
% 1.14/1.37 inference(modus_ponens,[status(thm)],[7364, 7363])).
% 1.14/1.37 tff(7366,plain,
% 1.14/1.37 ($false),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7365, 180, 543, 7359, 3017])).
% 1.14/1.37 tff(7367,plain,((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.37 tff(7368,plain,
% 1.14/1.37 (~r(s(s(z)), elem!1)),
% 1.14/1.37 inference(unit_resolution,[status(thm)],[7367, 7358, 543])).
% 1.14/1.38 tff(7369,plain,
% 1.14/1.38 (b(s(s(z)), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7107, 7368])).
% 1.14/1.38 tff(7370,plain,
% 1.14/1.38 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7008, 7369, 7342])).
% 1.14/1.38 tff(7371,plain,
% 1.14/1.38 (r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7023, 150, 7370, 7018])).
% 1.14/1.38 tff(7372,assumption,(r(s(s(s(s(z)))), z)), introduced(assumption)).
% 1.14/1.38 tff(7373,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7374,plain,
% 1.14/1.38 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7375,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7374])).
% 1.14/1.38 tff(7376,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.38 inference(transitivity,[status(thm)],[7375, 7373])).
% 1.14/1.38 tff(7377,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(7378,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[7377, 7376])).
% 1.14/1.38 tff(7379,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7378, 180, 543, 7359, 1691, 7372])).
% 1.14/1.38 tff(7380,plain,((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, elem!1)) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(7381,plain,
% 1.14/1.38 (~r(s(s(s(s(z)))), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7380, 7371, 7358, 543])).
% 1.14/1.38 tff(7382,plain,
% 1.14/1.38 (b(s(s(s(s(z)))), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7295, 7381])).
% 1.14/1.38 tff(7383,plain,
% 1.14/1.38 (~r(s(z), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[4984, 543, 169])).
% 1.14/1.38 tff(7384,plain,
% 1.14/1.38 (b(s(z), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[794, 7383])).
% 1.14/1.38 tff(7385,plain,
% 1.14/1.38 (~b(s(z), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2117, 206, 7384, 7382])).
% 1.14/1.38 tff(7386,plain,
% 1.14/1.38 (r(s(z), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7048, 7385])).
% 1.14/1.38 tff(7387,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7388,plain,
% 1.14/1.38 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7389,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7388])).
% 1.14/1.38 tff(7390,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.14/1.38 inference(transitivity,[status(thm)],[7389, 7387])).
% 1.14/1.38 tff(7391,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(7392,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[7391, 7390])).
% 1.14/1.38 tff(7393,plain,
% 1.14/1.38 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7392, 206, 7342, 7369])).
% 1.14/1.38 tff(7394,plain,
% 1.14/1.38 ((s(s(z)) = s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7193, 150, 7393])).
% 1.14/1.38 tff(7395,plain,
% 1.14/1.38 (r(s(s(z)), s(s(s(s(z)))))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7394, 7183])).
% 1.14/1.38 tff(7396,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7397,plain,
% 1.14/1.38 (((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7398,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7397])).
% 1.14/1.38 tff(7399,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[7398, 7396])).
% 1.14/1.38 tff(7400,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(z))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(7401,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(z)), s(s(s(s(z))))))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[7400, 7399])).
% 1.14/1.38 tff(7402,plain,
% 1.14/1.38 (~r(s(s(z)), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7401, 180, 7395, 7386])).
% 1.14/1.38 tff(7403,plain,
% 1.14/1.38 (b(s(s(z)), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7241, 150, 7402, 7065])).
% 1.14/1.38 tff(7404,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7405,plain,
% 1.14/1.38 (((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7406,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7405])).
% 1.14/1.38 tff(7407,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.38 inference(transitivity,[status(thm)],[7406, 7404])).
% 1.14/1.38 tff(7408,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(7409,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[7408, 7407])).
% 1.14/1.38 tff(7410,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7409, 206, 157, 7403, 7369])).
% 1.14/1.38 tff(7411,plain,((~b(elem!1, s(z))) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(7412,plain,
% 1.14/1.38 (~r(s(z), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7411, 7328, 7326])).
% 1.14/1.38 tff(7413,plain,
% 1.14/1.38 (b(s(z), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7084, 7412])).
% 1.14/1.38 tff(7414,plain,
% 1.14/1.38 (s(elem!1) = s(s(s(s(s(elem!1)))))),
% 1.14/1.38 inference(symmetry,[status(thm)],[6994])).
% 1.14/1.38 tff(7415,plain,
% 1.14/1.38 ((s(elem!1) = s(s(z))) <=> (s(s(s(s(s(elem!1))))) = s(s(z)))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7414])).
% 1.14/1.38 tff(7416,plain,
% 1.14/1.38 ((s(s(s(s(s(elem!1))))) = s(s(z))) <=> (s(elem!1) = s(s(z)))),
% 1.14/1.38 inference(symmetry,[status(thm)],[7415])).
% 1.14/1.38 tff(7417,plain,
% 1.14/1.38 ((~(s(s(s(s(s(elem!1))))) = s(s(z)))) <=> (~(s(elem!1) = s(s(z))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7416])).
% 1.14/1.38 tff(7418,plain,
% 1.14/1.38 (~(s(elem!1) = s(s(z)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2650, 7417])).
% 1.14/1.38 tff(7419,plain,
% 1.14/1.38 (~r(s(s(z)), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7262, 5860, 1691])).
% 1.14/1.38 tff(7420,plain,
% 1.14/1.38 (b(s(s(z)), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7107, 7419])).
% 1.14/1.38 tff(7421,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7422,plain,
% 1.14/1.38 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7423,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7422])).
% 1.14/1.38 tff(7424,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1)))),
% 1.14/1.38 inference(transitivity,[status(thm)],[7423, 7421])).
% 1.14/1.38 tff(7425,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(7426,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), elem!1))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[7425, 7424])).
% 1.14/1.38 tff(7427,plain,
% 1.14/1.38 (~b(s(s(z)), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7426, 206, 117, 7420])).
% 1.14/1.38 tff(7428,plain,
% 1.14/1.38 (r(s(s(z)), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7241, 150, 7427, 7065])).
% 1.14/1.38 tff(7429,plain,
% 1.14/1.38 (~r(s(s(z)), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[2150, 7428, 485])).
% 1.14/1.38 tff(7430,plain,
% 1.14/1.38 (b(s(s(z)), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7138, 150, 1951, 7429])).
% 1.14/1.38 tff(7431,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7432,plain,
% 1.14/1.38 (((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7433,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7432])).
% 1.14/1.38 tff(7434,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z)))),
% 1.14/1.38 inference(transitivity,[status(thm)],[7433, 7431])).
% 1.14/1.38 tff(7435,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(7436,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(z)), z))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[7435, 7434])).
% 1.14/1.38 tff(7437,plain,
% 1.14/1.38 (~b(s(elem!1), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7436, 206, 95, 7430])).
% 1.14/1.38 tff(7438,plain,
% 1.14/1.38 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7439,plain,
% 1.14/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(7440,plain,
% 1.14/1.38 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(z))) | b(s(elem!1), s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[7439, 7438])).
% 1.14/1.38 tff(7441,plain,
% 1.14/1.38 ((s(elem!1) = s(s(z))) | r(s(elem!1), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7440, 150, 7437])).
% 1.14/1.38 tff(7442,plain,
% 1.14/1.38 (r(s(elem!1), s(s(z)))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7441, 7418])).
% 1.14/1.38 tff(7443,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7444,plain,
% 1.14/1.38 (((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7445,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7444])).
% 1.14/1.38 tff(7446,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[7445, 7443])).
% 1.14/1.38 tff(7447,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), s(elem!1))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(7448,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[7447, 7446])).
% 1.14/1.38 tff(7449,plain,
% 1.14/1.38 (~b(s(s(s(s(z)))), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7448, 206, 95, 2200])).
% 1.14/1.38 tff(7450,assumption,(s(s(s(s(z)))) = s(elem!1)), introduced(assumption)).
% 1.14/1.38 tff(7451,plain,
% 1.14/1.38 (inj_0(s(s(s(s(z))))) = inj_0(s(elem!1))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7450])).
% 1.14/1.38 tff(7452,plain,
% 1.14/1.38 (s(s(s(z))) = s(s(s(s(s(s(elem!1))))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[1031, 7451, 7096, 71, 7095])).
% 1.14/1.38 tff(7453,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1341, 7452])).
% 1.14/1.38 tff(7454,plain,(~(s(s(s(s(z)))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(7455,plain,
% 1.14/1.38 (r(s(s(s(s(z)))), s(elem!1))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[6263, 150, 7454, 7449])).
% 1.14/1.38 tff(7456,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7457,plain,
% 1.14/1.38 (((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1)))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7458,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1)))))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7457])).
% 1.14/1.38 tff(7459,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.14/1.38 inference(transitivity,[status(thm)],[7458, 7456])).
% 1.14/1.38 tff(7460,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1))))),
% 1.14/1.38 inference(quant_inst,[status(thm)],[])).
% 1.14/1.38 tff(7461,plain,
% 1.14/1.38 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(elem!1), s(s(z)))) | (~r(s(s(s(s(z)))), s(elem!1)))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[7460, 7459])).
% 1.14/1.38 tff(7462,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7461, 180, 1691, 7455, 7442])).
% 1.14/1.38 tff(7463,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(elem!1), z)) | (~r(z, s(z))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(7464,plain,
% 1.14/1.38 (~b(s(elem!1), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7463, 7413, 7254, 485, 7330, 2200])).
% 1.14/1.38 tff(7465,plain,
% 1.14/1.38 (r(s(elem!1), z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[283, 7464])).
% 1.14/1.38 tff(7466,plain,
% 1.14/1.38 (~r(s(elem!1), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[6729, 7465, 7326])).
% 1.14/1.38 tff(7467,plain,
% 1.14/1.38 (~r(s(elem!1), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[3782, 7465, 485])).
% 1.14/1.38 tff(7468,plain,
% 1.14/1.38 ((s(s(s(elem!1))) = s(z)) <=> (s(elem!1) = s(z))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[6990])).
% 1.14/1.38 tff(7469,plain,
% 1.14/1.38 ((~(s(s(s(elem!1))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7468])).
% 1.14/1.38 tff(7470,plain,
% 1.14/1.38 (~(s(elem!1) = s(z))),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[427, 7469])).
% 1.14/1.38 tff(7471,plain,
% 1.14/1.38 (b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[1652, 7470])).
% 1.14/1.38 tff(7472,plain,
% 1.14/1.38 (b(s(elem!1), s(z))),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7471, 7467])).
% 1.14/1.38 tff(7473,plain,
% 1.14/1.38 (~b(s(elem!1), elem!1)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[4939, 7472, 7328])).
% 1.14/1.38 tff(7474,plain,
% 1.14/1.38 (s(elem!1) = elem!1),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[167, 7473, 7466])).
% 1.14/1.38 tff(7475,plain,
% 1.14/1.38 (r(s(elem!1), z) <=> r(elem!1, z)),
% 1.14/1.38 inference(monotonicity,[status(thm)],[31])).
% 1.14/1.38 tff(7476,plain,
% 1.14/1.38 (r(elem!1, z) <=> r(s(elem!1), z)),
% 1.14/1.38 inference(symmetry,[status(thm)],[7475])).
% 1.14/1.38 tff(7477,plain,
% 1.14/1.38 ((~r(elem!1, z)) <=> (~r(s(elem!1), z))),
% 1.14/1.38 inference(monotonicity,[status(thm)],[7476])).
% 1.14/1.38 tff(7478,plain,
% 1.14/1.38 (~r(s(elem!1), z)),
% 1.14/1.38 inference(modus_ponens,[status(thm)],[2792, 7477])).
% 1.14/1.38 tff(7479,plain,
% 1.14/1.38 ($false),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[270, 7478])).
% 1.14/1.38 tff(7480,plain,((~(s(elem!1) = elem!1)) | (~r(s(elem!1), z)) | r(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 1.14/1.38 tff(7481,plain,
% 1.14/1.38 (r(elem!1, z)),
% 1.14/1.38 inference(unit_resolution,[status(thm)],[7480, 7474, 7465])).
% 1.14/1.38 tff(7482,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7483,plain,
% 1.14/1.38 (((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.14/1.38 inference(rewrite,[status(thm)],[])).
% 1.14/1.38 tff(7484,plain,
% 1.14/1.38 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[7483])).
% 1.14/1.39 tff(7485,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.14/1.39 inference(transitivity,[status(thm)],[7484, 7482])).
% 1.14/1.39 tff(7486,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(7487,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7486, 7485])).
% 1.14/1.39 tff(7488,plain,
% 1.14/1.39 (~r(s(s(s(z))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7487, 180, 7481, 7233])).
% 1.14/1.39 tff(7489,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7490,plain,
% 1.14/1.39 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7491,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[7490])).
% 1.14/1.39 tff(7492,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.14/1.39 inference(transitivity,[status(thm)],[7491, 7489])).
% 1.14/1.39 tff(7493,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(7494,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7493, 7492])).
% 1.14/1.39 tff(7495,plain,
% 1.14/1.39 (~b(s(s(s(z))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7494, 206, 7328, 7164])).
% 1.14/1.39 tff(7496,plain,
% 1.14/1.39 ((s(s(s(z))) = elem!1) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[7097])).
% 1.14/1.39 tff(7497,plain,
% 1.14/1.39 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(z))) = elem!1)),
% 1.14/1.39 inference(symmetry,[status(thm)],[7496])).
% 1.14/1.39 tff(7498,plain,
% 1.14/1.39 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(z))) = elem!1))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[7497])).
% 1.14/1.39 tff(7499,plain,
% 1.14/1.39 (~(s(s(s(z))) = elem!1)),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[1341, 7498])).
% 1.14/1.39 tff(7500,plain,
% 1.14/1.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7501,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(7502,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7501, 7500])).
% 1.14/1.39 tff(7503,plain,
% 1.14/1.39 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7502, 150])).
% 1.14/1.39 tff(7504,plain,
% 1.14/1.39 (b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7503, 7499])).
% 1.14/1.39 tff(7505,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7504, 7495, 7488])).
% 1.14/1.39 tff(7506,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(7507,plain,
% 1.14/1.39 (~r(s(s(z)), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7506, 2200, 485, 4730])).
% 1.14/1.39 tff(7508,plain,
% 1.14/1.39 (b(s(s(z)), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7243, 7507])).
% 1.14/1.39 tff(7509,plain,
% 1.14/1.39 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7201, 206, 1732, 2200, 4730])).
% 1.14/1.39 tff(7510,plain,
% 1.14/1.39 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7212, 7509])).
% 1.14/1.39 tff(7511,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7512,plain,
% 1.14/1.39 (((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7513,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[7512])).
% 1.14/1.39 tff(7514,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[7513, 7511])).
% 1.14/1.39 tff(7515,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(7516,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7515, 7514])).
% 1.14/1.39 tff(7517,plain,
% 1.14/1.39 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7516, 206, 1732, 4730])).
% 1.14/1.39 tff(7518,plain,
% 1.14/1.39 ((s(s(s(s(z)))) = s(s(s(z)))) | b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1299, 150])).
% 1.14/1.39 tff(7519,plain,
% 1.14/1.39 (b(s(s(s(s(z)))), s(s(s(z)))) | r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7518, 7209])).
% 1.14/1.39 tff(7520,plain,
% 1.14/1.39 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7519, 7517])).
% 1.14/1.39 tff(7521,plain,
% 1.14/1.39 (~b(s(s(s(z))), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1792, 206, 1694, 1732])).
% 1.14/1.39 tff(7522,plain,
% 1.14/1.39 (r(s(s(s(z))), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7221, 7521])).
% 1.14/1.39 tff(7523,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7524,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(7525,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7524, 7523])).
% 1.14/1.39 tff(7526,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7525, 180, 7522, 1691, 7520, 7510])).
% 1.14/1.39 tff(7527,plain,((~b(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(7528,plain,
% 1.14/1.39 (~b(s(s(s(z))), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7527, 7254, 2200, 4730, 7508])).
% 1.14/1.39 tff(7529,plain,
% 1.14/1.39 (r(s(s(s(z))), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7163, 7528])).
% 1.14/1.39 tff(7530,plain,
% 1.14/1.39 (~r(z, s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[4723, 180, 485, 7529])).
% 1.14/1.39 tff(7531,plain,
% 1.14/1.39 (b(z, s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7132, 7530])).
% 1.14/1.39 tff(7532,plain,
% 1.14/1.39 (~b(s(s(s(s(z)))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7281, 157, 4730])).
% 1.14/1.39 tff(7533,plain,
% 1.14/1.39 (r(s(s(s(s(z)))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7272, 7532])).
% 1.14/1.39 tff(7534,plain,
% 1.14/1.39 (~r(s(s(z)), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7262, 7533, 1691])).
% 1.14/1.39 tff(7535,plain,
% 1.14/1.39 (b(s(s(z)), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7107, 7534])).
% 1.14/1.39 tff(7536,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7409, 206, 157, 1694, 7535])).
% 1.14/1.39 tff(7537,plain,((~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(7538,plain,
% 1.14/1.39 (~b(elem!1, s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7537, 7508, 7254, 4730])).
% 1.14/1.39 tff(7539,plain,
% 1.14/1.39 (r(elem!1, s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7168, 7538])).
% 1.14/1.39 tff(7540,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7541,plain,
% 1.14/1.39 (((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7542,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[7541])).
% 1.14/1.39 tff(7543,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[7542, 7540])).
% 1.14/1.39 tff(7544,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z))))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(7545,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(s(s(z)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7544, 7543])).
% 1.14/1.39 tff(7546,plain,
% 1.14/1.39 (~r(elem!1, s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7545, 180, 7539, 7529])).
% 1.14/1.39 tff(7547,plain,
% 1.14/1.39 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(commutativity,[status(thm)],[])).
% 1.14/1.39 tff(7548,plain,
% 1.14/1.39 ((elem!1 = s(s(s(z)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[7097])).
% 1.14/1.39 tff(7549,plain,
% 1.14/1.39 ((elem!1 = s(s(s(z)))) <=> (s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[7548, 7547])).
% 1.14/1.39 tff(7550,plain,
% 1.14/1.39 ((s(s(s(z))) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(z))))),
% 1.14/1.39 inference(symmetry,[status(thm)],[7549])).
% 1.14/1.39 tff(7551,plain,
% 1.14/1.39 ((~(s(s(s(z))) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(s(s(z)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[7550])).
% 1.14/1.39 tff(7552,plain,
% 1.14/1.39 (~(elem!1 = s(s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[1341, 7551])).
% 1.14/1.39 tff(7553,plain,
% 1.14/1.39 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7554,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(7555,plain,
% 1.14/1.39 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7554, 7553])).
% 1.14/1.39 tff(7556,plain,
% 1.14/1.39 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7555, 150])).
% 1.14/1.39 tff(7557,plain,
% 1.14/1.39 (b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7556, 7552])).
% 1.14/1.39 tff(7558,plain,
% 1.14/1.39 (b(elem!1, s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7557, 7546])).
% 1.14/1.39 tff(7559,plain,
% 1.14/1.39 (~r(z, elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7166, 7539, 485])).
% 1.14/1.39 tff(7560,plain,
% 1.14/1.39 (b(z, elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7290, 7559])).
% 1.14/1.39 tff(7561,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7562,plain,
% 1.14/1.39 (((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7563,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[7562])).
% 1.14/1.39 tff(7564,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[7563, 7561])).
% 1.14/1.39 tff(7565,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(7566,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7565, 7564])).
% 1.14/1.39 tff(7567,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7566, 206, 7560, 7558, 7531])).
% 1.14/1.39 tff(7568,plain,((~b(s(s(s(s(z)))), z)) | (~r(z, s(z))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(7569,plain,
% 1.14/1.39 (~b(s(s(s(s(z)))), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7568, 4730, 485])).
% 1.14/1.39 tff(7570,plain,
% 1.14/1.39 (r(s(s(s(s(z)))), z)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7295, 7569])).
% 1.14/1.39 tff(7571,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[6101, 180, 543, 5860, 7372])).
% 1.14/1.39 tff(7572,plain,((~r(z, elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(7573,plain,
% 1.14/1.39 (~r(s(s(s(s(z)))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7572, 543, 7570])).
% 1.14/1.39 tff(7574,plain,
% 1.14/1.39 (b(s(s(s(s(z)))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7272, 7573])).
% 1.14/1.39 tff(7575,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7281, 7574, 7169, 4730])).
% 1.14/1.39 tff(7576,plain,((~r(z, elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(7577,plain,
% 1.14/1.39 (~r(z, elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7576, 4730, 485])).
% 1.14/1.39 tff(7578,plain,
% 1.14/1.39 (b(z, elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7290, 7577])).
% 1.14/1.39 tff(7579,plain,
% 1.14/1.39 (~b(s(s(z)), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7324, 7141, 7578])).
% 1.14/1.39 tff(7580,plain,
% 1.14/1.39 (r(s(s(z)), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7107, 7579])).
% 1.14/1.39 tff(7581,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7582,plain,
% 1.14/1.39 (((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7583,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[7582])).
% 1.14/1.39 tff(7584,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[7583, 7581])).
% 1.14/1.39 tff(7585,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(7586,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7585, 7584])).
% 1.14/1.39 tff(7587,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7586, 180, 441, 1422, 3017])).
% 1.14/1.39 tff(7588,plain,((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(7589,plain,
% 1.14/1.39 (~r(elem!1, s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7588, 1422, 7580])).
% 1.14/1.39 tff(7590,plain,
% 1.14/1.39 (b(elem!1, s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7168, 7589])).
% 1.14/1.39 tff(7591,plain,
% 1.14/1.39 (~b(s(s(s(z))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7494, 206, 7590, 7164])).
% 1.14/1.39 tff(7592,plain,
% 1.14/1.39 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7591, 7122])).
% 1.14/1.39 tff(7593,plain,
% 1.14/1.39 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7516, 206, 7164, 4730])).
% 1.14/1.39 tff(7594,plain,
% 1.14/1.39 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7519, 7593])).
% 1.14/1.39 tff(7595,plain,
% 1.14/1.39 (~b(s(s(s(s(z)))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7281, 7590, 4730])).
% 1.14/1.39 tff(7596,plain,
% 1.14/1.39 (r(s(s(s(s(z)))), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7272, 7595])).
% 1.14/1.39 tff(7597,plain,
% 1.14/1.39 (r(s(s(s(s(z)))), s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7596, 6999])).
% 1.14/1.39 tff(7598,plain,
% 1.14/1.39 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[2197, 7597, 7594])).
% 1.14/1.39 tff(7599,plain,
% 1.14/1.39 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[1715, 7598])).
% 1.14/1.39 tff(7600,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7599, 7592])).
% 1.14/1.39 tff(7601,plain,((~r(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(7602,plain,
% 1.14/1.39 (~r(s(s(z)), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7601, 4730, 485])).
% 1.14/1.39 tff(7603,plain,
% 1.14/1.39 (b(s(s(z)), s(z))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7243, 7602])).
% 1.14/1.39 tff(7604,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7250, 206, 1694, 1263, 4730])).
% 1.14/1.39 tff(7605,plain,((~b(s(s(z)), s(z))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(7606,plain,
% 1.14/1.39 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7605, 7603, 4730])).
% 1.14/1.39 tff(7607,plain,
% 1.14/1.39 (r(s(s(s(s(z)))), s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7025, 7606])).
% 1.14/1.39 tff(7608,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7609,plain,
% 1.14/1.39 (((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7610,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[7609])).
% 1.14/1.39 tff(7611,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.39 inference(transitivity,[status(thm)],[7610, 7608])).
% 1.14/1.39 tff(7612,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z)))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(7613,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), z))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7612, 7611])).
% 1.14/1.39 tff(7614,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7613, 180, 7359, 1691, 7372])).
% 1.14/1.39 tff(7615,plain,((~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(s(z)))), z))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(7616,plain,
% 1.14/1.39 (~r(z, s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7615, 7607, 7570])).
% 1.14/1.39 tff(7617,plain,
% 1.14/1.39 (b(z, s(s(z)))),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7178, 7616])).
% 1.14/1.39 tff(7618,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7619,plain,
% 1.14/1.39 (((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))) <=> ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.14/1.39 inference(rewrite,[status(thm)],[])).
% 1.14/1.39 tff(7620,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))))),
% 1.14/1.39 inference(monotonicity,[status(thm)],[7619])).
% 1.14/1.39 tff(7621,plain,
% 1.14/1.39 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.14/1.39 inference(transitivity,[status(thm)],[7620, 7618])).
% 1.14/1.39 tff(7622,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z)))))),
% 1.14/1.39 inference(quant_inst,[status(thm)],[])).
% 1.14/1.39 tff(7623,plain,
% 1.14/1.39 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, s(s(z))))),
% 1.14/1.39 inference(modus_ponens,[status(thm)],[7622, 7621])).
% 1.14/1.39 tff(7624,plain,
% 1.14/1.39 ($false),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7623, 206, 797, 3555, 7348])).
% 1.14/1.39 tff(7625,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 1.14/1.39 tff(7626,plain,
% 1.14/1.39 (~b(s(s(z)), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7625, 7578, 7617])).
% 1.14/1.39 tff(7627,plain,
% 1.14/1.39 (r(s(s(z)), elem!1)),
% 1.14/1.39 inference(unit_resolution,[status(thm)],[7107, 7626])).
% 1.24/1.40 tff(7628,plain,
% 1.24/1.40 (~r(s(s(s(s(z)))), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7262, 7627, 7607])).
% 1.24/1.40 tff(7629,plain,
% 1.24/1.40 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7272, 7628])).
% 1.24/1.40 tff(7630,plain,
% 1.24/1.40 (~b(elem!1, s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7537, 7607, 7603, 4730])).
% 1.24/1.40 tff(7631,plain,
% 1.24/1.40 (r(elem!1, s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7168, 7630])).
% 1.24/1.40 tff(7632,plain,
% 1.24/1.40 (~r(elem!1, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7545, 180, 441, 2042])).
% 1.24/1.40 tff(7633,plain,
% 1.24/1.40 (b(elem!1, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7557, 7632])).
% 1.24/1.40 tff(7634,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7566, 206, 797, 7633, 7133])).
% 1.24/1.40 tff(7635,plain,((~r(s(s(s(z))), s(z))) | (~b(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(7636,plain,
% 1.24/1.40 (~r(s(s(s(z))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7635, 7578, 485, 7631])).
% 1.24/1.40 tff(7637,plain,
% 1.24/1.40 (b(s(s(s(z))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7163, 7636])).
% 1.24/1.40 tff(7638,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7639,plain,
% 1.24/1.40 (((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7640,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[7639])).
% 1.24/1.40 tff(7641,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[7640, 7638])).
% 1.24/1.40 tff(7642,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(7643,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[7642, 7641])).
% 1.24/1.40 tff(7644,plain,
% 1.24/1.40 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7643, 206, 7637, 7629, 4730])).
% 1.24/1.40 tff(7645,plain,
% 1.24/1.40 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7212, 7644])).
% 1.24/1.40 tff(7646,plain,
% 1.24/1.40 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7516, 206, 7637, 4730])).
% 1.24/1.40 tff(7647,plain,
% 1.24/1.40 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7519, 7646])).
% 1.24/1.40 tff(7648,plain,
% 1.24/1.40 (~b(s(s(s(z))), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[1792, 206, 7603, 7637])).
% 1.24/1.40 tff(7649,plain,
% 1.24/1.40 (r(s(s(s(z))), s(s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7221, 7648])).
% 1.24/1.40 tff(7650,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7525, 180, 7649, 7607, 7647, 7645])).
% 1.24/1.40 tff(7651,plain,((~b(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(7652,plain,
% 1.24/1.40 (~b(s(s(s(s(z)))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7651, 485])).
% 1.24/1.40 tff(7653,plain,
% 1.24/1.40 (r(s(s(s(s(z)))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7344, 7652])).
% 1.24/1.40 tff(7654,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7655,plain,
% 1.24/1.40 (((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7656,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[7655])).
% 1.24/1.40 tff(7657,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[7656, 7654])).
% 1.24/1.40 tff(7658,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(7659,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(s(s(s(z))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[7658, 7657])).
% 1.24/1.40 tff(7660,plain,
% 1.24/1.40 (~r(z, s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7659, 180, 485, 7653])).
% 1.24/1.40 tff(7661,plain,
% 1.24/1.40 ((z = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = z)),
% 1.24/1.40 inference(commutativity,[status(thm)],[])).
% 1.24/1.40 tff(7662,plain,
% 1.24/1.40 ((s(s(s(s(z)))) = z) <=> (z = s(s(s(s(z)))))),
% 1.24/1.40 inference(symmetry,[status(thm)],[7661])).
% 1.24/1.40 tff(7663,plain,
% 1.24/1.40 ((~(s(s(s(s(z)))) = z)) <=> (~(z = s(s(s(s(z))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[7662])).
% 1.24/1.40 tff(7664,plain,
% 1.24/1.40 (~(z = s(s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[2737, 7663])).
% 1.24/1.40 tff(7665,plain,
% 1.24/1.40 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7666,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(7667,plain,
% 1.24/1.40 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[7666, 7665])).
% 1.24/1.40 tff(7668,plain,
% 1.24/1.40 ((z = s(s(s(s(z))))) | b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7667, 150])).
% 1.24/1.40 tff(7669,plain,
% 1.24/1.40 (b(z, s(s(s(s(z))))) | r(z, s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7668, 7664])).
% 1.24/1.40 tff(7670,plain,
% 1.24/1.40 (b(z, s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7669, 7660])).
% 1.24/1.40 tff(7671,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7672,plain,
% 1.24/1.40 (((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7673,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[7672])).
% 1.24/1.40 tff(7674,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[7673, 7671])).
% 1.24/1.40 tff(7675,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(7676,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[7675, 7674])).
% 1.24/1.40 tff(7677,plain,
% 1.24/1.40 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7676, 180, 2042, 1119])).
% 1.24/1.40 tff(7678,plain,
% 1.24/1.40 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7518, 7677, 1689])).
% 1.24/1.40 tff(7679,plain,
% 1.24/1.40 (~r(s(s(s(s(z)))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7302, 180, 485, 1119])).
% 1.24/1.40 tff(7680,plain,
% 1.24/1.40 (b(s(s(s(s(z)))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7295, 7679])).
% 1.24/1.40 tff(7681,plain,
% 1.24/1.40 ($false),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[2206, 206, 7680, 7133, 7678])).
% 1.24/1.40 tff(7682,plain,((~r(s(s(s(z))), s(z))) | (s(s(s(s(z)))) = s(s(s(z)))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.40 tff(7683,plain,
% 1.24/1.40 ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7682, 7209])).
% 1.24/1.40 tff(7684,plain,
% 1.24/1.40 (~r(s(s(s(z))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7683, 7653, 485])).
% 1.24/1.40 tff(7685,plain,
% 1.24/1.40 (b(s(s(s(z))), s(z))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7163, 7684])).
% 1.24/1.40 tff(7686,plain,
% 1.24/1.40 (~b(s(s(s(z))), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7494, 206, 7169, 7685])).
% 1.24/1.40 tff(7687,plain,
% 1.24/1.40 (r(s(s(s(z))), elem!1)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7504, 7686])).
% 1.24/1.40 tff(7688,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7689,plain,
% 1.24/1.40 (((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z)))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7690,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[7689])).
% 1.24/1.40 tff(7691,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[7690, 7688])).
% 1.24/1.40 tff(7692,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(7693,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[7692, 7691])).
% 1.24/1.40 tff(7694,plain,
% 1.24/1.40 (~r(z, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7693, 180, 543, 7687])).
% 1.24/1.40 tff(7695,plain,
% 1.24/1.40 (b(z, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7132, 7694])).
% 1.24/1.40 tff(7696,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7697,plain,
% 1.24/1.40 (((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z))) <=> ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7698,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[7697])).
% 1.24/1.40 tff(7699,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 1.24/1.40 inference(transitivity,[status(thm)],[7698, 7696])).
% 1.24/1.40 tff(7700,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(z, elem!1)) | (~r(s(s(s(z))), z)))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(7701,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[7700, 7699])).
% 1.24/1.40 tff(7702,plain,
% 1.24/1.40 (~r(s(s(s(z))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7701, 180, 543, 7687])).
% 1.24/1.40 tff(7703,plain,
% 1.24/1.40 (b(s(s(s(z))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7232, 150, 1048, 7702])).
% 1.24/1.40 tff(7704,plain,
% 1.24/1.40 (~r(s(s(s(s(z)))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7302, 180, 485, 7653])).
% 1.24/1.40 tff(7705,plain,
% 1.24/1.40 (b(s(s(s(s(z)))), z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7295, 7704])).
% 1.24/1.40 tff(7706,plain,
% 1.24/1.40 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[5151, 206, 7705, 7703])).
% 1.24/1.40 tff(7707,plain,
% 1.24/1.40 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7519, 7706])).
% 1.24/1.40 tff(7708,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7709,plain,
% 1.24/1.40 (((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7710,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[7709])).
% 1.24/1.40 tff(7711,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[7710, 7708])).
% 1.24/1.40 tff(7712,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(7713,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[7712, 7711])).
% 1.24/1.40 tff(7714,plain,
% 1.24/1.40 (~b(elem!1, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7713, 206, 7169, 7685])).
% 1.24/1.40 tff(7715,plain,
% 1.24/1.40 (r(elem!1, s(s(s(z))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7557, 7714])).
% 1.24/1.40 tff(7716,plain,
% 1.24/1.40 (~(elem!1 = s(s(s(s(z)))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[7271, 6224])).
% 1.24/1.40 tff(7717,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7718,plain,
% 1.24/1.40 (((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7719,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[7718])).
% 1.24/1.40 tff(7720,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[7719, 7717])).
% 1.24/1.40 tff(7721,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z)))))))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(7722,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(s(z))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[7721, 7720])).
% 1.24/1.40 tff(7723,plain,
% 1.24/1.40 (~r(elem!1, s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7722, 180, 7707, 7715])).
% 1.24/1.40 tff(7724,plain,
% 1.24/1.40 ((elem!1 = s(s(s(s(z))))) | b(elem!1, s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[6275, 150, 7723])).
% 1.24/1.40 tff(7725,plain,
% 1.24/1.40 (b(elem!1, s(s(s(s(z)))))),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7724, 7716])).
% 1.24/1.40 tff(7726,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7727,plain,
% 1.24/1.40 (((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.40 inference(rewrite,[status(thm)],[])).
% 1.24/1.40 tff(7728,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[7727])).
% 1.24/1.40 tff(7729,plain,
% 1.24/1.40 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))))),
% 1.24/1.40 inference(transitivity,[status(thm)],[7728, 7726])).
% 1.24/1.40 tff(7730,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z)))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, z)))),
% 1.24/1.40 inference(quant_inst,[status(thm)],[])).
% 1.24/1.40 tff(7731,plain,
% 1.24/1.40 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(z, s(s(s(z))))) | (~b(z, s(s(s(s(z)))))) | (~b(elem!1, s(s(s(s(z))))))),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[7730, 7729])).
% 1.24/1.40 tff(7732,plain,
% 1.24/1.40 (~b(elem!1, z)),
% 1.24/1.40 inference(unit_resolution,[status(thm)],[7731, 206, 7695, 7670, 7725])).
% 1.24/1.40 tff(7733,plain,
% 1.24/1.40 ((s(s(elem!1)) = z) <=> (elem!1 = z)),
% 1.24/1.40 inference(transitivity,[status(thm)],[7287, 132])).
% 1.24/1.40 tff(7734,plain,
% 1.24/1.40 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = z))),
% 1.24/1.40 inference(monotonicity,[status(thm)],[7733])).
% 1.24/1.40 tff(7735,plain,
% 1.24/1.40 (~(elem!1 = z)),
% 1.24/1.40 inference(modus_ponens,[status(thm)],[224, 7734])).
% 1.24/1.41 tff(7736,plain,
% 1.24/1.41 (b(elem!1, z) | r(elem!1, z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[387, 7735])).
% 1.24/1.41 tff(7737,plain,
% 1.24/1.41 (r(elem!1, z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7736, 7732])).
% 1.24/1.41 tff(7738,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 1.24/1.41 tff(7739,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7740,plain,
% 1.24/1.41 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7741,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[7740])).
% 1.24/1.41 tff(7742,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.41 inference(transitivity,[status(thm)],[7741, 7739])).
% 1.24/1.41 tff(7743,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(7744,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[7743, 7742])).
% 1.24/1.41 tff(7745,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7744, 180, 2189, 7738])).
% 1.24/1.41 tff(7746,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7272, 7745])).
% 1.24/1.41 tff(7747,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 1.24/1.41 tff(7748,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7749,plain,
% 1.24/1.41 (((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7750,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[7749])).
% 1.24/1.41 tff(7751,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[7750, 7748])).
% 1.24/1.41 tff(7752,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(z)))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(7753,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[7752, 7751])).
% 1.24/1.41 tff(7754,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7753, 180, 2189, 7747])).
% 1.24/1.41 tff(7755,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7025, 7754])).
% 1.24/1.41 tff(7756,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7757,plain,
% 1.24/1.41 (((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7758,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[7757])).
% 1.24/1.41 tff(7759,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[7758, 7756])).
% 1.24/1.41 tff(7760,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(7761,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[7760, 7759])).
% 1.24/1.41 tff(7762,plain,
% 1.24/1.41 (~r(s(s(z)), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7761, 180, 374, 7747, 7738])).
% 1.24/1.41 tff(7763,plain,
% 1.24/1.41 (b(s(s(z)), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7107, 7762])).
% 1.24/1.41 tff(7764,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7008, 7763, 7755, 7746])).
% 1.24/1.41 tff(7765,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(7766,plain,
% 1.24/1.41 (~r(s(s(z)), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7765, 7737, 7715, 7707])).
% 1.24/1.41 tff(7767,plain,
% 1.24/1.41 (b(s(s(z)), s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7148, 7766])).
% 1.24/1.41 tff(7768,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7769,plain,
% 1.24/1.41 (((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7770,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[7769])).
% 1.24/1.41 tff(7771,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[7770, 7768])).
% 1.24/1.41 tff(7772,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(7773,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[7772, 7771])).
% 1.24/1.41 tff(7774,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7773, 206, 3556, 1694, 1732])).
% 1.24/1.41 tff(7775,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(7776,plain,
% 1.24/1.41 (~b(s(s(z)), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7775, 7767, 7685])).
% 1.24/1.41 tff(7777,plain,
% 1.24/1.41 (r(s(s(z)), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7243, 7776])).
% 1.24/1.41 tff(7778,plain,
% 1.24/1.41 (~r(s(s(z)), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[2150, 7777, 485])).
% 1.24/1.41 tff(7779,plain,
% 1.24/1.41 (b(s(s(z)), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7140, 7778])).
% 1.24/1.41 tff(7780,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7155, 206, 7767, 7779, 7695])).
% 1.24/1.41 tff(7781,plain,((~r(z, elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(7782,plain,
% 1.24/1.41 (~r(z, elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7781, 485])).
% 1.24/1.41 tff(7783,plain,
% 1.24/1.41 (b(z, elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7290, 7782])).
% 1.24/1.41 tff(7784,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7785,plain,
% 1.24/1.41 (((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z))))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7786,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[7785])).
% 1.24/1.41 tff(7787,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.41 inference(transitivity,[status(thm)],[7786, 7784])).
% 1.24/1.41 tff(7788,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, s(s(s(s(z)))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(7789,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[7788, 7787])).
% 1.24/1.41 tff(7790,plain,
% 1.24/1.41 (~b(z, s(s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7789, 206, 797, 2728])).
% 1.24/1.41 tff(7791,plain,
% 1.24/1.41 (r(z, s(s(s(s(z)))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7669, 7790])).
% 1.24/1.41 tff(7792,plain,
% 1.24/1.41 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7006, 206, 2728, 3555])).
% 1.24/1.41 tff(7793,plain,
% 1.24/1.41 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7023, 150, 7792, 7018])).
% 1.24/1.41 tff(7794,plain,
% 1.24/1.41 (~b(z, s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7623, 206, 797, 3555])).
% 1.24/1.41 tff(7795,plain,
% 1.24/1.41 (r(z, s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7178, 7794])).
% 1.24/1.41 tff(7796,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7797,plain,
% 1.24/1.41 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7798,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[7797])).
% 1.24/1.41 tff(7799,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[7798, 7796])).
% 1.24/1.41 tff(7800,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(7801,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(z, s(s(z)))) | (~r(z, s(s(s(s(z))))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[7800, 7799])).
% 1.24/1.41 tff(7802,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7801, 180, 7795, 7793, 7791])).
% 1.24/1.41 tff(7803,plain,((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(7804,plain,
% 1.24/1.41 (~b(s(s(s(s(z)))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7803, 3555, 797])).
% 1.24/1.41 tff(7805,plain,
% 1.24/1.41 (r(s(s(s(s(z)))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7272, 7804])).
% 1.24/1.41 tff(7806,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7807,plain,
% 1.24/1.41 (((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z)))) <=> ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7808,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[7807])).
% 1.24/1.41 tff(7809,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z)))))),
% 1.24/1.41 inference(transitivity,[status(thm)],[7808, 7806])).
% 1.24/1.41 tff(7810,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(z, s(s(z)))) | (~r(s(z), s(s(z)))) | (~r(z, s(z))))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(7811,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(z), s(s(z)))) | (~r(z, s(s(z))))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[7810, 7809])).
% 1.24/1.41 tff(7812,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7811, 180, 6456, 7795, 7072])).
% 1.24/1.41 tff(7813,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(7814,plain,
% 1.24/1.41 (~b(s(z), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7813, 3555, 797])).
% 1.24/1.41 tff(7815,plain,
% 1.24/1.41 (r(s(z), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7084, 7814])).
% 1.24/1.41 tff(7816,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[5874, 180, 7815, 7805, 1119])).
% 1.24/1.41 tff(7817,plain,((~b(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), s(z))) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(7818,plain,
% 1.24/1.41 (~b(s(s(z)), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7817, 7653, 7783])).
% 1.24/1.41 tff(7819,plain,
% 1.24/1.41 (r(s(s(z)), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7107, 7818])).
% 1.24/1.41 tff(7820,plain,
% 1.24/1.41 (~b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7235, 7141, 7705])).
% 1.24/1.41 tff(7821,plain,
% 1.24/1.41 (r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7025, 7820])).
% 1.24/1.41 tff(7822,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7262, 7821, 7819])).
% 1.24/1.41 tff(7823,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7272, 7822])).
% 1.24/1.41 tff(7824,plain,
% 1.24/1.41 (~b(s(z), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7304, 7823, 7783])).
% 1.24/1.41 tff(7825,plain,
% 1.24/1.41 (r(s(z), elem!1)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7084, 7824])).
% 1.24/1.41 tff(7826,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7312, 180, 7825, 1422, 7819])).
% 1.24/1.41 tff(7827,plain,((~r(s(s(z)), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(7828,plain,
% 1.24/1.41 (~r(s(s(z)), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7827, 485])).
% 1.24/1.41 tff(7829,plain,
% 1.24/1.41 (b(s(s(z)), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7243, 7828])).
% 1.24/1.41 tff(7830,plain,
% 1.24/1.41 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7262, 5860, 7819])).
% 1.24/1.41 tff(7831,plain,
% 1.24/1.41 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7025, 7830])).
% 1.24/1.41 tff(7832,plain,
% 1.24/1.41 (~b(s(s(z)), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7235, 7831, 7705])).
% 1.24/1.41 tff(7833,plain,
% 1.24/1.41 (r(s(s(z)), z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7140, 7832])).
% 1.24/1.41 tff(7834,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7835,plain,
% 1.24/1.41 (((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.24/1.41 inference(rewrite,[status(thm)],[])).
% 1.24/1.41 tff(7836,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[7835])).
% 1.24/1.41 tff(7837,plain,
% 1.24/1.41 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.24/1.41 inference(transitivity,[status(thm)],[7836, 7834])).
% 1.24/1.41 tff(7838,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))),
% 1.24/1.41 inference(quant_inst,[status(thm)],[])).
% 1.24/1.41 tff(7839,plain,
% 1.24/1.41 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 1.24/1.41 inference(modus_ponens,[status(thm)],[7838, 7837])).
% 1.24/1.41 tff(7840,plain,
% 1.24/1.41 ($false),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7839, 180, 374, 1312, 3017])).
% 1.24/1.41 tff(7841,plain,((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.41 tff(7842,plain,
% 1.24/1.41 (~r(elem!1, z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7841, 7833, 7819])).
% 1.24/1.41 tff(7843,plain,
% 1.24/1.41 (b(elem!1, z)),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7736, 7842])).
% 1.24/1.41 tff(7844,plain,
% 1.24/1.41 (~(s(s(s(s(z)))) = s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7208, 1692])).
% 1.24/1.41 tff(7845,plain,
% 1.24/1.41 (~r(s(s(s(z))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7682, 7844, 1119, 485])).
% 1.24/1.41 tff(7846,plain,
% 1.24/1.41 (b(s(s(s(z))), s(z))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7163, 7845])).
% 1.24/1.41 tff(7847,plain,
% 1.24/1.41 (~b(elem!1, s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7713, 206, 157, 7846])).
% 1.24/1.41 tff(7848,plain,
% 1.24/1.41 (r(elem!1, s(s(s(z))))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[7557, 7847])).
% 1.24/1.41 tff(7849,plain,
% 1.24/1.41 (~b(elem!1, s(s(z)))),
% 1.24/1.41 inference(unit_resolution,[status(thm)],[3277, 206, 157, 1694])).
% 1.24/1.41 tff(7850,plain,
% 1.24/1.41 ((elem!1 = s(s(z))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(z)))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[7097])).
% 1.24/1.41 tff(7851,plain,
% 1.24/1.41 ((s(s(s(s(s(s(elem!1)))))) = s(s(z))) <=> (elem!1 = s(s(z)))),
% 1.24/1.41 inference(symmetry,[status(thm)],[7850])).
% 1.24/1.41 tff(7852,plain,
% 1.24/1.41 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(z)))) <=> (~(elem!1 = s(s(z))))),
% 1.24/1.41 inference(monotonicity,[status(thm)],[7851])).
% 1.24/1.41 tff(7853,plain,
% 1.24/1.42 (~(elem!1 = s(s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[1111, 7852])).
% 1.24/1.42 tff(7854,plain,
% 1.24/1.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7855,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(7856,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[7855, 7854])).
% 1.24/1.42 tff(7857,plain,
% 1.24/1.42 ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7856, 150])).
% 1.24/1.42 tff(7858,plain,
% 1.24/1.42 (b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7857, 7853])).
% 1.24/1.42 tff(7859,plain,
% 1.24/1.42 (r(elem!1, s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7858, 7849])).
% 1.24/1.42 tff(7860,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7861,plain,
% 1.24/1.42 (((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7862,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[7861])).
% 1.24/1.42 tff(7863,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.42 inference(transitivity,[status(thm)],[7862, 7860])).
% 1.24/1.42 tff(7864,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(elem!1, z)) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(7865,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[7864, 7863])).
% 1.24/1.42 tff(7866,plain,
% 1.24/1.42 (~b(s(s(s(z))), elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7865, 206, 653, 157, 7846])).
% 1.24/1.42 tff(7867,plain,
% 1.24/1.42 (r(s(s(s(z))), elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7504, 7866])).
% 1.24/1.42 tff(7868,plain,
% 1.24/1.42 (~b(s(s(s(z))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1792, 206, 1694, 7846])).
% 1.24/1.42 tff(7869,plain,
% 1.24/1.42 (r(s(s(s(z))), s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1307, 7868, 1692])).
% 1.24/1.42 tff(7870,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7871,plain,
% 1.24/1.42 (((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7872,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[7871])).
% 1.24/1.42 tff(7873,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z)))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[7872, 7870])).
% 1.24/1.42 tff(7874,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(7875,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), s(s(z)))) | (~r(elem!1, s(s(z))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[7874, 7873])).
% 1.24/1.42 tff(7876,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7875, 180, 7869, 7867, 7859, 7848])).
% 1.24/1.42 tff(7877,plain,((s(s(s(z))) = s(s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(7878,plain,
% 1.24/1.42 ((~b(s(s(z)), s(z))) | (~b(elem!1, z)) | (~b(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(z, s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7877, 7145])).
% 1.24/1.42 tff(7879,plain,
% 1.24/1.42 (~b(elem!1, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7878, 7843, 7653, 7829, 485])).
% 1.24/1.42 tff(7880,plain,
% 1.24/1.42 (r(elem!1, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7168, 7879])).
% 1.24/1.42 tff(7881,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7882,plain,
% 1.24/1.42 (((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7883,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[7882])).
% 1.24/1.42 tff(7884,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.42 inference(transitivity,[status(thm)],[7883, 7881])).
% 1.24/1.42 tff(7885,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(7886,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[7885, 7884])).
% 1.24/1.42 tff(7887,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7886, 180, 7880, 5860, 7653])).
% 1.24/1.42 tff(7888,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(7889,plain,
% 1.24/1.42 (~r(s(s(s(s(z)))), elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7888, 485])).
% 1.24/1.42 tff(7890,plain,
% 1.24/1.42 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7272, 7889])).
% 1.24/1.42 tff(7891,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7789, 206, 7783, 7890, 7670])).
% 1.24/1.42 tff(7892,plain,(~r(z, s(z))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(7893,plain,
% 1.24/1.42 (b(z, s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[505, 7892])).
% 1.24/1.42 tff(7894,plain,
% 1.24/1.42 ((~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7356, 7893])).
% 1.24/1.42 tff(7895,plain,
% 1.24/1.42 (~b(z, s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7894, 7120])).
% 1.24/1.42 tff(7896,plain,
% 1.24/1.42 (r(z, s(s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7178, 7895])).
% 1.24/1.42 tff(7897,plain,
% 1.24/1.42 (~r(s(s(s(s(z)))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7615, 7896, 7026])).
% 1.24/1.42 tff(7898,plain,
% 1.24/1.42 (b(s(s(s(s(z)))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7295, 7897])).
% 1.24/1.42 tff(7899,plain,
% 1.24/1.42 (~r(s(z), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[4984, 7085, 543])).
% 1.24/1.42 tff(7900,plain,
% 1.24/1.42 (b(s(z), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[794, 7899])).
% 1.24/1.42 tff(7901,plain,
% 1.24/1.42 (~b(s(z), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2117, 206, 7900, 7898])).
% 1.24/1.42 tff(7902,plain,
% 1.24/1.42 (r(s(z), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7048, 7901])).
% 1.24/1.42 tff(7903,plain,
% 1.24/1.42 (~b(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7392, 206, 2728, 3555])).
% 1.24/1.42 tff(7904,plain,
% 1.24/1.42 ((s(s(z)) = s(s(s(s(z))))) | r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7193, 150, 7903])).
% 1.24/1.42 tff(7905,plain,
% 1.24/1.42 (r(s(s(z)), s(s(s(s(z)))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7904, 7183])).
% 1.24/1.42 tff(7906,plain,
% 1.24/1.42 (~r(s(s(z)), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7401, 180, 7905, 7902])).
% 1.24/1.42 tff(7907,plain,
% 1.24/1.42 (b(s(s(z)), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7243, 7906])).
% 1.24/1.42 tff(7908,plain,
% 1.24/1.42 ((~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(z)))), s(s(s(s(s(s(elem!1))))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1710, 7209, 7145])).
% 1.24/1.42 tff(7909,plain,
% 1.24/1.42 (~b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7908, 7907, 7032, 7029, 7026])).
% 1.24/1.42 tff(7910,plain,
% 1.24/1.42 (r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[1715, 7909])).
% 1.24/1.42 tff(7911,plain,
% 1.24/1.42 (r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(s(z))), elem!1)),
% 1.24/1.42 inference(monotonicity,[status(thm)],[6996])).
% 1.24/1.42 tff(7912,plain,
% 1.24/1.42 (r(s(s(s(z))), elem!1) <=> r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(symmetry,[status(thm)],[7911])).
% 1.24/1.42 tff(7913,plain,
% 1.24/1.42 ((~r(s(s(s(z))), elem!1)) <=> (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[7912])).
% 1.24/1.42 tff(7914,assumption,(~r(s(s(s(z))), elem!1)), introduced(assumption)).
% 1.24/1.42 tff(7915,plain,
% 1.24/1.42 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[7914, 7913])).
% 1.24/1.42 tff(7916,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[2168, 7915])).
% 1.24/1.42 tff(7917,plain,(r(s(s(s(z))), elem!1) | (~r(s(s(s(z))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(7918,plain,
% 1.24/1.42 (r(s(s(s(z))), elem!1)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7917, 7910])).
% 1.24/1.42 tff(7919,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7920,plain,
% 1.24/1.42 (((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z)))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7921,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[7920])).
% 1.24/1.42 tff(7922,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.42 inference(transitivity,[status(thm)],[7921, 7919])).
% 1.24/1.42 tff(7923,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(7924,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[7923, 7922])).
% 1.24/1.42 tff(7925,plain,
% 1.24/1.42 (~r(s(z), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7924, 180, 7085, 7918])).
% 1.24/1.42 tff(7926,plain,
% 1.24/1.42 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 1.24/1.42 inference(commutativity,[status(thm)],[])).
% 1.24/1.42 tff(7927,plain,
% 1.24/1.42 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 1.24/1.42 inference(symmetry,[status(thm)],[7926])).
% 1.24/1.42 tff(7928,plain,
% 1.24/1.42 ((~(s(s(s(z))) = s(z))) <=> (~(s(z) = s(s(s(z)))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[7927])).
% 1.24/1.42 tff(7929,plain,
% 1.24/1.42 (~(s(z) = s(s(s(z))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[7162, 7928])).
% 1.24/1.42 tff(7930,plain,
% 1.24/1.42 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7931,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(7932,plain,
% 1.24/1.42 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[7931, 7930])).
% 1.24/1.42 tff(7933,plain,
% 1.24/1.42 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7932, 150])).
% 1.24/1.42 tff(7934,plain,
% 1.24/1.42 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7933, 7929])).
% 1.24/1.42 tff(7935,plain,
% 1.24/1.42 (b(s(z), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7934, 7925])).
% 1.24/1.42 tff(7936,plain,
% 1.24/1.42 (~r(z, s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7693, 180, 543, 7918])).
% 1.24/1.42 tff(7937,plain,
% 1.24/1.42 (b(z, s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7132, 7936])).
% 1.24/1.42 tff(7938,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7939,plain,
% 1.24/1.42 (((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7940,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[7939])).
% 1.24/1.42 tff(7941,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[7940, 7938])).
% 1.24/1.42 tff(7942,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(z))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(7943,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(z, s(s(s(z)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[7942, 7941])).
% 1.24/1.42 tff(7944,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7943, 206, 7893, 7937, 7935])).
% 1.24/1.42 tff(7945,plain,((~r(s(s(s(s(z)))), s(z))) | (~r(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(7946,plain,
% 1.24/1.42 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7945, 3555, 2728, 543])).
% 1.24/1.42 tff(7947,plain,
% 1.24/1.42 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7344, 7946])).
% 1.24/1.42 tff(7948,plain,
% 1.24/1.42 (~b(s(s(s(s(z)))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[6109, 206, 7893, 7947])).
% 1.24/1.42 tff(7949,plain,
% 1.24/1.42 (r(s(s(s(s(z)))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7295, 7948])).
% 1.24/1.42 tff(7950,plain,
% 1.24/1.42 (~b(s(s(s(s(z)))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[6109, 206, 911, 4730])).
% 1.24/1.42 tff(7951,plain,
% 1.24/1.42 (r(s(s(s(s(z)))), z)),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7295, 7950])).
% 1.24/1.42 tff(7952,plain,
% 1.24/1.42 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7518, 7517, 7209])).
% 1.24/1.42 tff(7953,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7954,plain,
% 1.24/1.42 (((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))) <=> ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7955,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[7954])).
% 1.24/1.42 tff(7956,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.24/1.42 inference(transitivity,[status(thm)],[7955, 7953])).
% 1.24/1.42 tff(7957,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z))))))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(7958,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(s(z))), s(z))) | (~b(z, s(s(s(z)))))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[7957, 7956])).
% 1.24/1.42 tff(7959,plain,
% 1.24/1.42 (~b(z, s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7958, 206, 911, 1732])).
% 1.24/1.42 tff(7960,plain,
% 1.24/1.42 (r(z, s(s(s(z))))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7132, 7959])).
% 1.24/1.42 tff(7961,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7962,plain,
% 1.24/1.42 (((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.42 inference(rewrite,[status(thm)],[])).
% 1.24/1.42 tff(7963,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))))),
% 1.24/1.42 inference(monotonicity,[status(thm)],[7962])).
% 1.24/1.42 tff(7964,plain,
% 1.24/1.42 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.42 inference(transitivity,[status(thm)],[7963, 7961])).
% 1.24/1.42 tff(7965,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.42 inference(quant_inst,[status(thm)],[])).
% 1.24/1.42 tff(7966,plain,
% 1.24/1.42 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.42 inference(modus_ponens,[status(thm)],[7965, 7964])).
% 1.24/1.42 tff(7967,plain,
% 1.24/1.42 ($false),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7966, 180, 7960, 7952, 7951])).
% 1.24/1.42 tff(7968,plain,((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.42 tff(7969,plain,
% 1.24/1.42 ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7968, 7893])).
% 1.24/1.42 tff(7970,plain,
% 1.24/1.42 (~b(s(s(s(z))), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7969, 7947])).
% 1.24/1.42 tff(7971,plain,
% 1.24/1.42 (r(s(s(s(z))), s(z))),
% 1.24/1.42 inference(unit_resolution,[status(thm)],[7163, 7970])).
% 1.24/1.42 tff(7972,plain,
% 1.24/1.42 (~b(elem!1, s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7281, 7947, 2728])).
% 1.24/1.43 tff(7973,plain,
% 1.24/1.43 (r(elem!1, s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7168, 7972])).
% 1.24/1.43 tff(7974,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(7975,plain,
% 1.24/1.43 (((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1))) <=> ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(7976,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[7975])).
% 1.24/1.43 tff(7977,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[7976, 7974])).
% 1.24/1.43 tff(7978,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(7979,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[7978, 7977])).
% 1.24/1.43 tff(7980,plain,
% 1.24/1.43 (~r(s(s(s(z))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7979, 180, 7973, 7971])).
% 1.24/1.43 tff(7981,plain,
% 1.24/1.43 (b(s(s(s(z))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7504, 7980])).
% 1.24/1.43 tff(7982,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(7983,plain,
% 1.24/1.43 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(7984,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[7983])).
% 1.24/1.43 tff(7985,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[7984, 7982])).
% 1.24/1.43 tff(7986,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(7987,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[7986, 7985])).
% 1.24/1.43 tff(7988,plain,
% 1.24/1.43 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7987, 206, 2728, 7981])).
% 1.24/1.43 tff(7989,plain,
% 1.24/1.43 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7212, 7988])).
% 1.24/1.43 tff(7990,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(7991,plain,
% 1.24/1.43 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(7992,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[7991])).
% 1.24/1.43 tff(7993,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[7992, 7990])).
% 1.24/1.43 tff(7994,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(7995,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(z)), elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[7994, 7993])).
% 1.24/1.43 tff(7996,plain,
% 1.24/1.43 (~b(s(s(s(z))), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7995, 206, 7981, 3555])).
% 1.24/1.43 tff(7997,plain,
% 1.24/1.43 (r(s(s(s(z))), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7221, 7996])).
% 1.24/1.43 tff(7998,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(7999,plain,
% 1.24/1.43 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8000,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[7999])).
% 1.24/1.43 tff(8001,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[8000, 7998])).
% 1.24/1.43 tff(8002,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(8003,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[8002, 8001])).
% 1.24/1.43 tff(8004,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8003, 180, 7997, 7026, 7989, 7949])).
% 1.24/1.43 tff(8005,plain,((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(8006,plain,
% 1.24/1.43 (~b(s(s(z)), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8005, 2728, 543])).
% 1.24/1.43 tff(8007,plain,
% 1.24/1.43 (r(s(s(z)), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7107, 8006])).
% 1.24/1.43 tff(8008,plain,
% 1.24/1.43 (~r(z, s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7693, 180, 543, 3474])).
% 1.24/1.43 tff(8009,plain,
% 1.24/1.43 (b(z, s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7132, 8008])).
% 1.24/1.43 tff(8010,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8011,plain,
% 1.24/1.43 (((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z))) <=> ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8012,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[8011])).
% 1.24/1.43 tff(8013,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[8012, 8010])).
% 1.24/1.43 tff(8014,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(s(s(z)), z)))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(8015,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[8014, 8013])).
% 1.24/1.43 tff(8016,plain,
% 1.24/1.43 (~r(s(s(z)), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8015, 180, 543, 3017])).
% 1.24/1.43 tff(8017,plain,
% 1.24/1.43 (b(s(s(z)), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7140, 8016])).
% 1.24/1.43 tff(8018,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8019,plain,
% 1.24/1.43 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8020,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[8019])).
% 1.24/1.43 tff(8021,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[8020, 8018])).
% 1.24/1.43 tff(8022,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(8023,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[8022, 8021])).
% 1.24/1.43 tff(8024,plain,
% 1.24/1.43 (~r(s(s(z)), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8023, 180, 3017, 3474])).
% 1.24/1.43 tff(8025,plain,
% 1.24/1.43 (b(s(s(z)), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7148, 8024])).
% 1.24/1.43 tff(8026,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7155, 206, 8025, 8017, 8009])).
% 1.24/1.43 tff(8027,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(8028,plain,
% 1.24/1.43 (~r(s(s(s(z))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8027, 8007, 543])).
% 1.24/1.43 tff(8029,plain,
% 1.24/1.43 (b(s(s(s(z))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7504, 8028])).
% 1.24/1.43 tff(8030,plain,
% 1.24/1.43 (~r(z, s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7367, 8007, 543])).
% 1.24/1.43 tff(8031,plain,
% 1.24/1.43 (b(z, s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7178, 8030])).
% 1.24/1.43 tff(8032,plain,
% 1.24/1.43 (~b(s(z), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7894, 8031])).
% 1.24/1.43 tff(8033,plain,
% 1.24/1.43 (r(s(z), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7071, 8032])).
% 1.24/1.43 tff(8034,plain,
% 1.24/1.43 (~r(s(z), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7093, 8033, 8007])).
% 1.24/1.43 tff(8035,plain,
% 1.24/1.43 (b(s(z), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7084, 8034])).
% 1.24/1.43 tff(8036,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8037,plain,
% 1.24/1.43 (((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8038,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[8037])).
% 1.24/1.43 tff(8039,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[8038, 8036])).
% 1.24/1.43 tff(8040,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(8041,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[8040, 8039])).
% 1.24/1.43 tff(8042,plain,
% 1.24/1.43 (~b(s(z), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8041, 206, 8035, 8029])).
% 1.24/1.43 tff(8043,plain,
% 1.24/1.43 (r(s(z), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7934, 8042])).
% 1.24/1.43 tff(8044,assumption,(b(s(s(s(s(z)))), s(s(s(z))))), introduced(assumption)).
% 1.24/1.43 tff(8045,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8046,plain,
% 1.24/1.43 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8047,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[8046])).
% 1.24/1.43 tff(8048,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 1.24/1.43 inference(transitivity,[status(thm)],[8047, 8045])).
% 1.24/1.43 tff(8049,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(8050,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z))))) | (~b(s(s(s(s(z)))), elem!1))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[8049, 8048])).
% 1.24/1.43 tff(8051,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8050, 206, 2728, 2920, 8044])).
% 1.24/1.43 tff(8052,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(8053,plain,
% 1.24/1.43 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8052, 8029, 2728])).
% 1.24/1.43 tff(8054,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7519, 8053])).
% 1.24/1.43 tff(8055,plain,
% 1.24/1.43 (~b(s(s(s(s(z)))), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[6121, 206, 8035, 2728])).
% 1.24/1.43 tff(8056,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), s(z))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7344, 8055])).
% 1.24/1.43 tff(8057,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8058,plain,
% 1.24/1.43 (((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z)))) <=> ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8059,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))))),
% 1.24/1.43 inference(monotonicity,[status(thm)],[8058])).
% 1.24/1.43 tff(8060,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.43 inference(transitivity,[status(thm)],[8059, 8057])).
% 1.24/1.43 tff(8061,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))))),
% 1.24/1.43 inference(quant_inst,[status(thm)],[])).
% 1.24/1.43 tff(8062,plain,
% 1.24/1.43 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(s(z)))), s(s(s(z)))))),
% 1.24/1.43 inference(modus_ponens,[status(thm)],[8061, 8060])).
% 1.24/1.43 tff(8063,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8062, 180, 8056, 8054, 8043])).
% 1.24/1.43 tff(8064,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(8065,plain,
% 1.24/1.43 (~b(s(s(s(s(z)))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8064, 543])).
% 1.24/1.43 tff(8066,plain,
% 1.24/1.43 (r(s(s(s(s(z)))), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7272, 8065])).
% 1.24/1.43 tff(8067,plain,
% 1.24/1.43 (~r(s(z), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7340, 8066, 543])).
% 1.24/1.43 tff(8068,plain,
% 1.24/1.43 (b(s(z), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7084, 8067])).
% 1.24/1.43 tff(8069,plain,
% 1.24/1.43 (~r(s(s(s(s(z)))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7572, 8066, 543])).
% 1.24/1.43 tff(8070,plain,
% 1.24/1.43 (b(s(s(s(s(z)))), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7295, 8069])).
% 1.24/1.43 tff(8071,plain,
% 1.24/1.43 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7262, 3017, 8066])).
% 1.24/1.43 tff(8072,plain,
% 1.24/1.43 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7025, 8071])).
% 1.24/1.43 tff(8073,plain,
% 1.24/1.43 (~b(s(s(z)), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7235, 8072, 8070])).
% 1.24/1.43 tff(8074,plain,
% 1.24/1.43 (r(s(s(z)), z)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7140, 8073])).
% 1.24/1.43 tff(8075,plain,
% 1.24/1.43 ($false),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8015, 180, 543, 8074, 3017])).
% 1.24/1.43 tff(8076,plain,((~r(s(s(z)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.43 tff(8077,plain,
% 1.24/1.43 (~r(s(s(z)), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8076, 543])).
% 1.24/1.43 tff(8078,plain,
% 1.24/1.43 (b(s(s(z)), elem!1)),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7107, 8077])).
% 1.24/1.43 tff(8079,plain,
% 1.24/1.43 (~b(s(z), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[8041, 206, 117, 2920])).
% 1.24/1.43 tff(8080,plain,
% 1.24/1.43 (r(s(z), s(s(s(z))))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7934, 8079])).
% 1.24/1.43 tff(8081,plain,
% 1.24/1.43 (~b(s(s(s(z))), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7995, 206, 2920, 3555])).
% 1.24/1.43 tff(8082,plain,
% 1.24/1.43 (r(s(s(s(z))), s(s(z)))),
% 1.24/1.43 inference(unit_resolution,[status(thm)],[7221, 8081])).
% 1.24/1.43 tff(8083,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8084,plain,
% 1.24/1.43 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.43 inference(rewrite,[status(thm)],[])).
% 1.24/1.43 tff(8085,plain,
% 1.24/1.43 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[8084])).
% 1.24/1.44 tff(8086,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[8085, 8083])).
% 1.24/1.44 tff(8087,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(8088,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[8087, 8086])).
% 1.24/1.44 tff(8089,plain,
% 1.24/1.44 (~b(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8088, 206, 117, 2920])).
% 1.24/1.44 tff(8090,plain,
% 1.24/1.44 (r(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7163, 8089])).
% 1.24/1.44 tff(8091,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8092,plain,
% 1.24/1.44 (((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8093,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[8092])).
% 1.24/1.44 tff(8094,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[8093, 8091])).
% 1.24/1.44 tff(8095,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(8096,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(s(z))), s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[8095, 8094])).
% 1.24/1.44 tff(8097,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8096, 180, 8090, 8082, 7072, 8080])).
% 1.24/1.44 tff(8098,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(8099,plain,
% 1.24/1.44 (~b(s(s(s(z))), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8098, 8078, 8068])).
% 1.24/1.44 tff(8100,plain,
% 1.24/1.44 (r(s(s(s(z))), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7504, 8099])).
% 1.24/1.44 tff(8101,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8102,plain,
% 1.24/1.44 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z)))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8103,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[8102])).
% 1.24/1.44 tff(8104,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[8103, 8101])).
% 1.24/1.44 tff(8105,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(8106,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), s(s(s(z))))) | (~r(s(s(s(s(z)))), elem!1))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[8105, 8104])).
% 1.24/1.44 tff(8107,plain,
% 1.24/1.44 (~r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8106, 180, 8066, 8100])).
% 1.24/1.44 tff(8108,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7519, 8107])).
% 1.24/1.44 tff(8109,plain,
% 1.24/1.44 (~r(z, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7693, 180, 543, 8100])).
% 1.24/1.44 tff(8110,plain,
% 1.24/1.44 (b(z, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7132, 8109])).
% 1.24/1.44 tff(8111,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2206, 206, 8070, 8110, 8108])).
% 1.24/1.44 tff(8112,plain,(~r(z, elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(8113,plain,
% 1.24/1.44 (b(z, elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7290, 8112])).
% 1.24/1.44 tff(8114,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[6454, 206, 117, 797, 911])).
% 1.24/1.44 tff(8115,plain,((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(8116,plain,
% 1.24/1.44 (~b(s(z), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8115, 797, 911])).
% 1.24/1.44 tff(8117,plain,
% 1.24/1.44 (r(s(z), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7084, 8116])).
% 1.24/1.44 tff(8118,plain,
% 1.24/1.44 (~b(s(z), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7356, 7348, 911])).
% 1.24/1.44 tff(8119,plain,
% 1.24/1.44 (r(s(z), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7071, 8118])).
% 1.24/1.44 tff(8120,plain,
% 1.24/1.44 (~r(s(s(z)), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7093, 8119, 8117])).
% 1.24/1.44 tff(8121,plain,
% 1.24/1.44 (b(s(s(z)), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7107, 8120])).
% 1.24/1.44 tff(8122,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7623, 206, 797, 8121, 7348])).
% 1.24/1.44 tff(8123,plain,((~b(z, s(s(z)))) | (~b(z, elem!1)) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(8124,plain,
% 1.24/1.44 ((~b(z, s(s(z)))) | (~b(z, elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8123, 7893])).
% 1.24/1.44 tff(8125,plain,
% 1.24/1.44 (~b(z, s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8124, 8113])).
% 1.24/1.44 tff(8126,plain,
% 1.24/1.44 (r(z, s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7178, 8125])).
% 1.24/1.44 tff(8127,plain,
% 1.24/1.44 ((~b(z, elem!1)) | (~b(s(z), elem!1))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8115, 7893])).
% 1.24/1.44 tff(8128,plain,
% 1.24/1.44 (~b(s(z), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8127, 8113])).
% 1.24/1.44 tff(8129,plain,
% 1.24/1.44 (r(s(z), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7084, 8128])).
% 1.24/1.44 tff(8130,plain,
% 1.24/1.44 (~r(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[5874, 180, 8129, 5860])).
% 1.24/1.44 tff(8131,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7344, 8130])).
% 1.24/1.44 tff(8132,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8133,plain,
% 1.24/1.44 (((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8134,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[8133])).
% 1.24/1.44 tff(8135,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[8134, 8132])).
% 1.24/1.44 tff(8136,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(s(s(z)))), s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(8137,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), s(z)))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[8136, 8135])).
% 1.24/1.44 tff(8138,plain,
% 1.24/1.44 (~b(s(s(s(s(z)))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8137, 206, 8113, 7893, 8131])).
% 1.24/1.44 tff(8139,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7295, 8138])).
% 1.24/1.44 tff(8140,plain,
% 1.24/1.44 (~r(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7615, 8139, 8126])).
% 1.24/1.44 tff(8141,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7025, 8140])).
% 1.24/1.44 tff(8142,plain,
% 1.24/1.44 (~b(s(s(z)), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7605, 8141, 8131])).
% 1.24/1.44 tff(8143,plain,
% 1.24/1.44 (r(s(s(z)), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7243, 8142])).
% 1.24/1.44 tff(8144,plain,
% 1.24/1.44 (~b(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7969, 8131])).
% 1.24/1.44 tff(8145,plain,
% 1.24/1.44 (r(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7163, 8144])).
% 1.24/1.44 tff(8146,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8147,plain,
% 1.24/1.44 (((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8148,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[8147])).
% 1.24/1.44 tff(8149,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[8148, 8146])).
% 1.24/1.44 tff(8150,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z)))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(8151,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(s(z))), s(s(z))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[8150, 8149])).
% 1.24/1.44 tff(8152,plain,
% 1.24/1.44 (~r(s(s(s(z))), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8151, 180, 8145, 8143])).
% 1.24/1.44 tff(8153,plain,
% 1.24/1.44 (b(s(s(s(z))), s(s(z)))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7221, 8152])).
% 1.24/1.44 tff(8154,plain,
% 1.24/1.44 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1269, 206, 8153, 8141])).
% 1.24/1.44 tff(8155,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7519, 8154])).
% 1.24/1.44 tff(8156,plain,
% 1.24/1.44 (~r(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2197, 8155, 7000])).
% 1.24/1.44 tff(8157,plain,
% 1.24/1.44 (b(s(s(s(z))), s(s(s(s(s(s(elem!1)))))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[1715, 8156])).
% 1.24/1.44 tff(8158,plain,
% 1.24/1.44 (b(s(s(s(z))), elem!1)),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[8157, 6997])).
% 1.24/1.44 tff(8159,plain,
% 1.24/1.44 (~b(z, s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2664, 206, 7893, 8131])).
% 1.24/1.44 tff(8160,plain,
% 1.24/1.44 (r(z, s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7669, 8159])).
% 1.24/1.44 tff(8161,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8162,plain,
% 1.24/1.44 (((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8163,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[8162])).
% 1.24/1.44 tff(8164,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[8163, 8161])).
% 1.24/1.44 tff(8165,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(8166,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[8165, 8164])).
% 1.24/1.44 tff(8167,plain,
% 1.24/1.44 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8166, 206, 8153, 8141])).
% 1.24/1.44 tff(8168,plain,
% 1.24/1.44 (r(s(s(s(z))), s(s(s(s(z)))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7212, 8167])).
% 1.24/1.44 tff(8169,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8170,plain,
% 1.24/1.44 (((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z)))))) <=> ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8171,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[8170])).
% 1.24/1.44 tff(8172,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[8171, 8169])).
% 1.24/1.44 tff(8173,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z)))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(z))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(8174,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(z))))) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(z, s(s(s(s(z))))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[8173, 8172])).
% 1.24/1.44 tff(8175,plain,
% 1.24/1.44 (~r(z, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8174, 180, 8168, 8160])).
% 1.24/1.44 tff(8176,plain,
% 1.24/1.44 (b(z, s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7132, 8175])).
% 1.24/1.44 tff(8177,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 1.24/1.44 tff(8178,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8179,plain,
% 1.24/1.44 (((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8180,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[8179])).
% 1.24/1.44 tff(8181,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 1.24/1.44 inference(transitivity,[status(thm)],[8180, 8178])).
% 1.24/1.44 tff(8182,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(8183,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[8182, 8181])).
% 1.24/1.44 tff(8184,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8183, 206, 8113, 2920, 8177])).
% 1.24/1.44 tff(8185,plain,((~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(8186,plain,
% 1.24/1.44 (~b(s(s(s(z))), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8185, 8176])).
% 1.24/1.44 tff(8187,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8186, 8158])).
% 1.24/1.44 tff(8188,plain,(~r(s(s(s(s(z)))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(8189,plain,
% 1.24/1.44 (b(s(s(s(s(z)))), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7272, 8188])).
% 1.24/1.44 tff(8190,plain,
% 1.24/1.44 (~b(s(s(s(s(z)))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[2734, 206, 8113, 8189])).
% 1.24/1.44 tff(8191,plain,
% 1.24/1.44 (r(s(s(s(s(z)))), z)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7295, 8190])).
% 1.24/1.44 tff(8192,plain,
% 1.24/1.44 (~b(s(s(z)), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7803, 8189, 8113])).
% 1.24/1.44 tff(8193,plain,
% 1.24/1.44 (r(s(s(z)), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7107, 8192])).
% 1.24/1.44 tff(8194,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7312, 180, 8129, 1422, 3017])).
% 1.24/1.44 tff(8195,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(8196,plain,
% 1.24/1.44 (~r(s(s(z)), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8195, 8193])).
% 1.24/1.44 tff(8197,plain,
% 1.24/1.44 (b(s(s(z)), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7243, 8196])).
% 1.24/1.44 tff(8198,plain,
% 1.24/1.44 (~r(s(s(z)), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8023, 180, 8193, 3474])).
% 1.24/1.44 tff(8199,plain,
% 1.24/1.44 (b(s(s(z)), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7148, 8198])).
% 1.24/1.44 tff(8200,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8201,plain,
% 1.24/1.44 (((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z)))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.44 inference(rewrite,[status(thm)],[])).
% 1.24/1.44 tff(8202,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))))),
% 1.24/1.44 inference(monotonicity,[status(thm)],[8201])).
% 1.24/1.44 tff(8203,plain,
% 1.24/1.44 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1)))),
% 1.24/1.44 inference(transitivity,[status(thm)],[8202, 8200])).
% 1.24/1.44 tff(8204,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))))),
% 1.24/1.44 inference(quant_inst,[status(thm)],[])).
% 1.24/1.44 tff(8205,plain,
% 1.24/1.44 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~r(X1, X3)) | (~r(X0, X3)) | (~r(X1, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), elem!1))),
% 1.24/1.44 inference(modus_ponens,[status(thm)],[8204, 8203])).
% 1.24/1.44 tff(8206,plain,
% 1.24/1.44 (~r(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8205, 180, 8129, 3474])).
% 1.24/1.44 tff(8207,plain,
% 1.24/1.44 (b(s(s(s(z))), s(z))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7163, 8206])).
% 1.24/1.44 tff(8208,plain,
% 1.24/1.44 ($false),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7775, 8207, 8199, 8197])).
% 1.24/1.44 tff(8209,plain,(~r(s(s(s(z))), elem!1)), inference(lemma,lemma(discharge,[]))).
% 1.24/1.44 tff(8210,plain,
% 1.24/1.44 (b(s(s(s(z))), elem!1)),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[7504, 8209])).
% 1.24/1.44 tff(8211,plain,
% 1.24/1.44 (~b(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.44 inference(unit_resolution,[status(thm)],[8052, 8210, 8189])).
% 1.24/1.45 tff(8212,plain,
% 1.24/1.45 (r(s(s(s(s(z)))), s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[7519, 8211])).
% 1.24/1.45 tff(8213,plain,
% 1.24/1.45 (~b(z, s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[8185, 8210])).
% 1.24/1.45 tff(8214,plain,
% 1.24/1.45 (r(z, s(s(s(z))))),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[7132, 8213])).
% 1.24/1.45 tff(8215,plain,
% 1.24/1.45 ($false),
% 1.24/1.45 inference(unit_resolution,[status(thm)],[7966, 180, 8214, 8212, 8191])).
% 1.24/1.45 % SZS output end Proof
% 1.24/1.45 % E exiting
%------------------------------------------------------------------------------